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New invariants for integral latticesMar 20 2019Let $\Lambda$ be any integral lattice in Euclidean space. It has been shown that for every integer $n>0$, there is a hypersphere that passes through exactly $n$ points of $\Lambda$. Using this result, we introduce new lattice invariants and give some ... More
Subrearrangement-invariant function spacesMar 10 2019Rearrangement-invariance in function spaces can be viewed as a kind of generalization of 1-symmetry for Schauder bases. We define subrearrangement-invariance in function spaces as an analogous generalization of 1-subsymmetry. It is then shown that every ... More
Capacities and 1-strict subsets in metric spacesMar 07 2019In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$. Relying on the ... More
Random Sturm-Liouville Operators with Point InteractionsMar 07 2019We study invariance for eigenvalues of families of selfadjoint Sturm-Liouville operators with local point interactions. In a probabilistic setting, we show that a point is either an eigenvalue for all members of the family or only for a set of measure ... More
Locally small spaces with an applicationMar 03 2019We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.
Construction Methods for GaussoidsFeb 28 2019The number of $n$-gaussoids is shown to be a double exponential function in $n$. The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing $3$-minors and encoding the resulting combinatorial constraints ... More
$\mathcal G$-systemsFeb 25 2019Mar 03 2019A $\mathcal G$-system is a collection of $\mathbb Z$-bases of $\mathbb Z^n$ with some extra axiomatic conditions. There are two kinds of actions "mutations" and "twists" naturally acting on a $\mathcal G$-system, which provide the combinatorial structure ... More
$\mathcal G$-systemsFeb 25 2019A $\mathcal G$-system is a collection of $\mathbb Z$-bases of $\mathbb Z^n$ with some extra axiomatic conditions. There are two kinds of actions "mutations" and "twists" naturally acting on a $\mathcal G$-system, which provide the combinatorial structure ... More
The Absolute Orders on the Coxeter Groups $A_n$ and $B_n$ are SpernerFeb 22 2019Over 50 years ago, Rota posted the following celebrated `Research Problem': prove or disprove that the partial order of partitions on an $n$-set (i.e., the refinement order) is Sperner. A counterexample was eventually discovered by Canfield in 1978. However, ... More
Non-linear functionals, deficient topological measures, and representation theorems on locally compact spacesFeb 15 2019We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topological measures and topological measures on locally compact spaces. We prove ... More
Generalized semimodularity: order statisticsFeb 14 2019A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th Cartesian power ... More
Operational causality in spacetimeFeb 13 2019We consider the general evolution of binary statistics in a, possibly curved, spacetime with the help of the optimal transport theory. It covers a wide range of models including classical statistics, quantum wave-packets and general, possibly non-linear, ... More
The double point formula with isolated singularities and canonical embeddingsFeb 12 2019Motivated by the embedding problem of canonical models in small codimension, we extend Severi's double point formula to the case of surfaces with rational double points, and we give more general double point formulae for varieties with isolated singularities. ... More
The minimal cone of an algebraic Laurent seriesFeb 11 2019For a given Laurent series that is algebraic over the field of power series in several indeterminates over a characteristic zero field, we show that the convex hull of its support is essentially a polyhedral rational cone. One of the main tools for proving ... More
The minimal cone of an algebraic Laurent seriesFeb 11 2019Mar 08 2019For a given Laurent series that is algebraic over the field of power series in several indeterminates over a characteristic zero field, we show that the convex hull of its support is essentially a polyhedral rational cone. One of the main tools for proving ... More
Derivator Six-Functor-Formalisms - Construction IIFeb 10 2019Starting from very simple and obviously necessary axioms on a (derivator enhanced) four-functor-formalism, we construct derivator six-functor-formalisms using compactifications. This works, for example, for various contexts over topological spaces and ... More
Beyond Sperner's lemmaFeb 03 2019The present paper is devoted to a recent beautiful and ingenious proof of Brouwer's fixed point theorem due to mathematical economists H. Petri and M. Voorneveld. The heart of this proof is an analogue of Sperner's lemma motivated by Shapley-Scarf model ... More
The Jacobian, reflection arrangement and discriminant for reflection Hopf algebrasFeb 01 2019We study finite dimensional semisimple Hopf algebra actions on noetherian connected graded Artin-Schelter regular algebras, and introduce definitions of the Jacobian, the reflection arrangement and the discriminant in a noncommutative setting.
On the topological structure of the Hahn field and convergence of power seriesJan 26 2019In this paper, we study the topological structure of the Hahn field whose elements are functions from the additive abelian group of rational numbers to the real numbers field, with well-ordered support. After reviewing the algebraic and order structures ... More
Certain results on Euler-type integrals and their applicationsJan 22 2019This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite integrals. Further, ... More
Degree of rational maps via specializationJan 19 2019Feb 04 2019One considers the behavior of the degree of a rational map under specialization of the coefficients of the defining linear system. The method rests on the classical idea of Kronecker as applied to the context of projective schemes and their specializations. ... More
Instability of unidirectional flows for the 2D $α$-Euler equationsJan 05 2019Jan 21 2019We study stability of unidirectional flows for the linearized 2D $\alpha$-Euler equations on the torus. The unidirectional flows are steady states whose vorticity is given by Fourier modes corresponding to a vector $\mathbf p \in \mathbb Z^{2}$. We linearize ... More
Dynamics of the $a$-map over residually finite Dedekind Domains and applicationsJan 04 2019Let $\mathfrak D$ be a residually finite Dedekind domain, $a\in \mathfrak D$ be a nonzero element and $\mathfrak n$ be a nonzero ideal of $\mathfrak D$. In this paper we describe the dynamics of the map $x\mapsto ax$ over the quotient ring $\mathfrak ... More
Is the Symmetric Group Sperner?Jan 01 2019Jan 03 2019An antichain $\mathcal{A}$ in a poset $\mathcal{P}$ is a subset of $\mathcal{P}$ in which no two elements are comparable. Sperner showed that the maximal antichain in the Boolean lattice, $\mathcal{B}_n = \left\{ 0 < 1 \right\}^n$, is the largest rank ... More
Functions Holomorphic over Finite-Dimensional Commutative Associative Algebras 1: One-Variable Local Theory IDec 31 2018Jan 01 2019We study in detail the one-variable local theory of functions holomorphic over a finite-dimensional commutative associative unital $\mathbb{C}$-algebra $\mathcal{A}$, showing that it shares a multitude of features with the classical one-variable Complex ... More
Discrete convolutions of BV functions in quasiopen sets in metric spacesDec 24 2018We study fine potential theory and in particular partitions of unity in quasiopen sets in the case $p=1$. Using these, we develop an analog of the discrete convolution technique in quasiopen (instead of open) sets. We apply this technique to show that ... More
Min-max formulas for nonlocal elliptic operators on Euclidean spaceDec 23 2018An operator satisfies the Global Comparison Property if anytime a function touches another from above at some point, then the operator preserves the ordering at the point of contact. This is characteristic of degenerate elliptic operators, including nonlocal ... More
Invariant hypersurfacesDec 20 2018The following theorem, which includes as very special cases results of Jouanolou and Hrushovski on algebraic $D$-varieties on the one hand, and of Cantat on rational dynamics on the other, is established: Working over a field of characteristic zero, suppose ... More
Homology groups of cubical sets with connectionsDec 18 2018Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of "connection" as a new kind of degeneracy. In this paper, for a cubical set with connections, we show that the connections generate an acyclic subcomplex of ... More
A De Bruijn-Erdős theorem in graphs?Dec 15 2018A set of $n$ points in the Euclidean plane determines at least $n$ distinct lines unless these $n$ points are collinear. In 2006, Chen and Chv\'atal asked whether the same statement holds true in general metric spaces, where the line determined by points ... More
A panorama of positivityDec 13 2018This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). ... More
Effective Łojasiewicz gradient inequality and finite determinacy of non-isolated Nash function singularitiesDec 12 2018Let $X\subset \mathbb{R}^n$ be a compact semialgebraic set and let $f:X\to \mathbb{R}$ be a nonzero Nash function. We give a Solern\'o and D'Acunto-Kurdyka type estimation of the exponent $\varrho\in[0,1)$ in the {\L}ojasiewicz gradient inequality $|\nabla ... More
On the Component Factor Group G/G_0 of a Pro-Lie Group GDec 12 2018A pro-Lie group $G$ is a topological group such that $G$ is isomorphic to the projective limit of all quotient groups $G/N$ (modulo closed normal subgroups $N$) such that $G/N$ is a finite dimensional real Lie group. A topological group is almost connected ... More
A space with a Lusin $π$-base whose square has no Lusin $π$-baseDec 09 2018We construct a space ${X}$ that has a Lusin $\pi$-base and such that ${X}^{2}$ has no Lusin $\pi$-base.
A Conjectured Integer Sequence Arising From the Exponential IntegralDec 02 2018Dec 15 2018Let $f_0(z) = \exp(z/(1-z))$, $f_1(z) = \exp(1/(1-z))E_1(1/(1-z))$, where $E_1(x) = \int_x^\infty e^{-t}t^{-1}{\,d}t$. Let $a_n = [z^n]f_0(z)$ and $b_n = [z^n]f_1(z)$ be the corresponding Maclaurin series coefficients. We show that $a_n$ and $b_n$ may ... More
On the Nash problem for surfaces in positive characteristicDec 01 2018This paper seeks to prove the bijectivity of the "Nash mapping" from the set of irreducible components of the scheme parametrizing analytic arcs on an algebraic surface $X$ whose origin is a singular point, into the set of irreducible components of the ... More
A systematic path to non-Markovian dynamics: New generalized FPK equations for dynamical systems under coloured noise excitation with arbitrary correlation functionNov 29 2018Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic dynamics, advanced ... More
An alternative foundation and the generalized continuum hypothesisNov 27 2018In this paper I introduce a new and intuitive first-order foundational theory (where the concept of set is not primitive) and use it to show that the power set of an infinite set does not exist. In particular, proofs of uncountability of a set are essentially ... More
2-step nilpotent Lie groups and hyperbolic automorphismsNov 20 2018A connected Lie group admitting an expansive automorphism is known to be nilpotent but all nilpotent Lie groups do not admit expansive automorphisms. In this article, we find sufficient conditions for 2-step nilpotent Lie groups to admit expansive automorphisms. ... More
User-Friendly Sparse Matrices with Hybrid Storage and Template-Based Expression OptimisationNov 20 2018Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage format. In ... More
CGW-categoriesNov 19 2018We introduce a new perspective on the $K$-theory of exact categories via the notion of a CGW-category. CGW-categories are a generalization of exact categories that admit a Qullen $Q$-construction, but which also include examples such as finite sets and ... More
Quantifier free definable relations on finite dimensional subspace lattices with involutionNov 19 2018Jan 22 2019For finite dimensional hermitean inner product spaces $V$, over $*$-fields $F$, and in the presence of orthogonal bases providing form elements in the prime subfield of $F$, we show that quantifier free definable relations in the subspace lattice $L(V)$ ... More
Eigenvalues of symmetrized shuffling operatorsNov 17 2018Feb 27 2019This paper describes a combinatorial way of obtaining all the eigenvalues of the symmetrized shuffling operators introduced by Victor Reiner, Franco Saliola and Volkmar Welker. It allows us to prove their conjecture that these eigenvalues are integers. ... More
Eigenvalues of symmetrized shuffling operatorsNov 17 2018This paper describes a combinatorial way of obtaining all the eigenvalues of the symmetrized shuffling operators introduced by Victor Reiner, Franco Saliola and Volkmar Welker. It allows us to prove their conjecture that these eigenvalues are integers. ... More
A sharp Leibniz rule for BV functions in metric spacesNov 15 2018We prove a Leibniz rule for BV functions in a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality. Unlike in previous versions of the rule, we do not assume the functions to be locally essentially bounded ... More
Extensions of the Novikov-Furutsu theorem, obtained by using Volterra functional calculusNov 15 2018Mar 07 2019Novikov-Furutsu (NF) theorem is a well-known mathematical tool, used in stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the product of a random functional with a Gaussian argument multiplied by the argument itself. ... More
Extensions of the Novikov-Furutsu theorem, obtained by using Volterra functional calculusNov 15 2018Novikov-Furutsu (NF) theorem is a well-known mathematical tool, used in stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the product of a random functional with a Gaussian argument multiplied by the argument itself. ... More
Factoring Non-negative Operator Valued Trigonometric Polynomials in Two VariablesNov 14 2018Nov 21 2018Using Schur complement techniques, it is shown that a non-negative operator valued trigonometric polynomial in two variables with degree (d_1,d_2) can be written as a finite sum of hermitian squares of at most 2d_2 analytic polynomials with degrees at ... More
The CDE property for skew vexillary permutationsNov 06 2018Nov 19 2018We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order intervals corresponding to certain vexillary permutations have the coincidental down-degree expectations (CDE) property. Actually our theorem applies more generally ... More
Quasi-random number generators for multivariate distributions based on generative neural networksNov 01 2018Generative moment matching networks are introduced as quasi-random number generators for multivariate distributions. So far, quasi-random number generators for non-uniform multivariate distributions require a careful design, often need to exploit specific ... More
The Affordable Care Act and the IRS Iterative Fixed Point ProcedureOct 31 2018We model the quantities appearing in Internal Revenue Service (IRS) tax guidance for calculating the health insurance premium tax credit created by the Patient Protection and Affordable Care Act, also called Obamacare. We ask the question of whether there ... More
Friezes satisfying higher SL$_k$-determinantsOct 24 2018In this article, we construct SL$_k$-friezes using Pl\"ucker coordinates, making use of the cluster structure on the homogeneous coordinate ring of the Grassmannian of $k$-spaces in $n$-space via the Pl\"ucker embedding. When this cluster algebra is of ... More
Compatibility and attainability of matrices of correlation-based measures of concordanceOct 16 2018Necessary and sufficient conditions are derived under which concordance measures arise from correlations of transformed ranks of random variables. Compatibility and attainability of square matrices with entries given by such measures are studied, that ... More
Compatibility and attainability of matrices of correlation-based measures of concordanceOct 16 2018Mar 18 2019Measures of concordance have been widely used in insurance and risk management to summarize non-linear dependence among risks modeled by random variables, which Pearson's correlation coefficient cannot capture. However, popular measures of concordance, ... More
Non-binary treebased unrooted phylogenetic networks and their relations to binary and rooted onesOct 16 2018Oct 17 2018Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of non-treelike evolutionary events such as hybridization. Typically, such networks have been analyzed based on their `level', i.e. based on the complexity ... More
Classes of treebased networksOct 16 2018Oct 17 2018Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the \emph{base tree}, by adding additional edges. ... More
Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spacesOct 12 2018In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a $1$-Poincar\'e inequality. We show that at almost every point $x$ outside the Cantor and jump parts of a BV ... More
On Isoclasses of Maximal Subalgebras Determined by AutomorphismsOct 01 2018Let $k$ be an algebraically-closed field, and let $B = kQ/I$ be a basic, finite-dimensional associative $k$-algebra with $n := \dim_kB < \infty$. Previous work shows that the collection of maximal subalgebras of $B$ carries the structure of a projective ... More
On Isoclasses of Maximal Subalgebras Determined by AutomorphismsOct 01 2018Feb 21 2019Let $k$ be an algebraically-closed field, and let $B = kQ/I$ be a basic, finite-dimensional associative $k$-algebra with $n := \dim_kB < \infty$. Previous work shows that the collection of maximal subalgebras of $B$ carries the structure of a projective ... More
Relations de Hodge--Riemann et combinatoire des matroïdes (d'après K. Adiprasito, J. Huh et E. Katz)Sep 25 2018Finite matroids are combinatorial structures that express the concept of linear independence. In 1964, G.-C. Rota conjectured that the coefficients of the "characteristic polynomial" of a matroid $M$, polynomial whose coefficients enumerate its subsets ... More
In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial idealsSep 24 2018The aim of this paper is to study the associated primes of powers of squarefree monomial ideals. Hypergraphs and squarefree monomial ideals are strongly connected. The cover ideal $J(H)$ of a hypergraph $H$ is the intersection of the primes corresponding ... More
The Liouville theorem for $p$-harmonic functions and quasiminimizers with finite energySep 19 2018We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite $p$th power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global $p$-Poincar\'e ... More
Quasi-periodic perturbations of heteroclinic attractor networksSep 16 2018We consider heteroclinic attractor networks motivated by models of competition between neural populations during binocular rivalry. We show that Gamma distributions of dominance times observed experimentally in binocular rivalry and other forms of bistable ... More
Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a $1$-Poincaré inequalitySep 11 2018We consider two notions of functions of bounded variation in complete metric measure spaces, one due to Martio and the other due to Miranda~Jr. We show that these two notions coincide, if the measure is doubling and supports a $1$-Poincar\'e inequality. ... More
Heat Flow with Dirichlet Boundary Conditions via Optimal Transport and Gluing of Metric Measure SpacesSep 04 2018We introduce the transportation-annihilation distance $W_p^\sharp$ between subprobabilities and derive contraction estimates with respect to this distance for the heat flow with homogeneous Dirichlet boundary conditions on an open set in a metric measure ... More
Non-commutative manifolds, the free square root and symmetric functions in two non-commuting variablesAug 30 2018The richly developed theory of complex manifolds plays important roles in our understanding of holomorphic functions in several complex variables. It is natural to consider manifolds that will play similar roles in the theory of holomorphic functions ... More
Blow-up for the pointwise NLS in dimension two: absence of critical powerAug 30 2018Nov 13 2018We consider the Schr\"odinger equation in dimension two with a fixed, pointwise, focusing nonlinearity and show the occurrence of a blow-up phenomenon with two peculiar features: first, the energy threshold under which all solutions blow up is strictly ... More
On a class of norms generated by nonnegative integrable distributionsAug 24 2018We show that any distribution function on $\mathbb{R}^d$ with nonnegative, nonzero and integrable marginal distributions can be characterized by a norm on $\mathbb{R}^{d+1}$, called $F$-norm. We characterize the set of $F$-norms and prove that pointwise ... More
On a conjecture for $\aleph_0$-bounded groupsAug 23 2018We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [8] holds while the classical Borel Conjecture fails.
The structure of random automorphisms of the rational numbersAug 16 2018In order to understand the structure of the "typical" element of an automorphism group, one has to study how large the conjugacy classes of the group are. For the case when typical is meant in the sense of Baire category, Truss proved that there is a ... More
Convex Union Representability and Convex CodesAug 12 2018We introduce and investigate $d$-convex union representable complexes: the complexes that arise as the nerve of a finite collection of convex open sets in $\mathbb R^d$ whose union is also convex. Chen, Frick, and Shiu recently proved that such complexes ... More
Ultradifferentiable CR manifoldsAug 08 2018In this article the notion of ultradifferentiable CR manifold is introduced and an ultradifferentiable regularity result for finitely nondegenerate CR mappings is proven. Here ultradifferentiable means with respect to Denjoy-Carleman classes defined by ... More
Nuisance Parameters Free Changepoint Detection in Non-stationary SeriesAug 06 2018Aug 13 2018Detecting abrupt changes in the mean of a time series, so-called changepoints, is important for many applications. However, many procedures rely on the estimation of nuisance parameters (like long-run variance). Under the alternative (a change in mean), ... More
A formula for the cohomology and $K$-class of a regular Hessenberg varietyAug 06 2018Hessenberg varieties are subvarieties of the flag variety parametrized by a linear operator $X$ and a nondecreasing function $h$. The family of Hessenberg varieties for regular $X$ is particularly important: they are used in quantum cohomology, in combinatorial ... More
Goursat completionsAug 04 2018We characterize categories with weak finite limits whose regular completions give rise to Goursat categories.
Combinatorics of the Deodhar decomposition of the GrassmannianJul 24 2018The Deodhar decomposition of the Grassmannian is a refinement of the Schubert, Richardson, and positroid stratifications of the Grassmannian. Go-diagrams are certain fillings of Ferrers diagrams with black stones, white stones, and pluses which index ... More
Onto Interpolation for the Dirichlet Space and for $W^{1,2}(\mathbb{D})$Jul 21 2018Nov 14 2018We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of capacity of some condensers. The same condition in fact characterizes all onto interpolating sequences for $ W^{1,2}(\mathbb{D}) ... More
The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg propertyJul 21 2018Prime end boundaries $\partial_P\Omega$ of domains $\Omega$ are studied in the setting of complete doubling metric measure spaces supporting a $p$-Poincar\'e inequality. Notions of rectifiably (in)accessible- and (in)finitely far away prime ends are introduced ... More
On graphs with 2 trivial distance idealsJul 20 2018Jul 24 2018Distance ideals generalize the Smith normal form of the distance matrix of a graph. The family of graphs with 2 trivial distance ideals contains the family of graphs whose distance matrix has at most 2 invariant factors equal to 1. Here we give an infinite ... More
Explicit inverse of nonsingular Jacobi matricesJul 17 2018We present here the necessary and sufficient conditions for the invertibility of tridiagonal matrices, commonly named Jacobi matrices, and explicitly compute their inverse. The techniques we use are related with the solution of Sturm-Liouville boundary ... More
Arc spaces, motivic measure and Lipschitz geometry of real algebraic setsJul 13 2018Dec 14 2018We investigate connections between Lipschitz geometry of real algebraic varieties and properties of their arc spaces. For this purpose we develop motivic integration in the real algebraic set-up. We construct a motivic measure on the space of real analytic ... More
L-infinity Formality check for the Hochschild Complex of Certain Universal Enveloping AlgebrasJul 09 2018We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more detail so(3)), and ... More
Lambert-W solves the noncommutative $Φ^4$-modelJul 09 2018Nov 04 2018The closed Dyson-Schwinger equation for the 2-point function of the noncommutative $\lambda \phi^4_2$-model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables. We prove an exact formula for a solution ... More
The combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials of lower intervalsJul 06 2018The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and generalizes, among ... More
Interpolating factorizations for acyclic Donaldson--Thomas invariantsJul 05 2018Mar 04 2019We prove a family of factorization formulas for the combinatorial Donaldson--Thomas invariant for an acyclic quiver. A quantum dilogarithm identity due to Reineke, later interpreted by Rimanyi by counting codimensions of quiver loci, gives two extremal ... More
Interpolating factorizations for acyclic Donaldson--Thomas invariantsJul 05 2018Jul 15 2018We prove a family of factorization formulas for the combinatorial Donaldson--Thomas invariant for an acyclic quiver. A quantum dilogarithm identity due to Reineke, later interpreted by Rim\'anyi by counting codimensions of quiver loci, gives two extremal ... More
Normality conditions of structures in coarse geometry and an alternative description of coarse proximitiesJul 02 2018Dec 23 2018We introduce an alternative description of coarse proximities. We define a coarse normality condition for connected coarse spaces and show that this definition agrees with large scale normality defined in [3] and asymptotic normality defined in [7]. We ... More
Normality conditions of structures in coarse geometry and an alternative description of coarse proximitiesJul 02 2018Feb 28 2019We introduce an alternative description of coarse proximities. We define a coarse normality condition for connected coarse spaces and show that this definition agrees with large scale normality defined in [3] and asymptotic normality defined in [7]. We ... More
Rule Algebras for Adhesive CategoriesJul 02 2018Feb 04 2019We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative in a natural sense. Notably, our results ... More
On the integrability of strongly regular graphsJun 29 2018Koolen et al. showed that if a connected graph with smallest eigenvalue at least $-3$ has large minimal valency, then it is $2$-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.
A class of generalized graph groups defined by balanced presentationsJun 27 2018We consider groups defined by non-empty balanced presentations with the property that each relator is of the form R(x,y), where x and y are distinct generators and R(.,.) is determined by some fixed cyclically reduced word R(a,b) that involves both a ... More
Distance covariance for discretized stochastic processesJun 25 2018Nov 29 2018Given an iid sequence of pairs of stochastic processes on the unit interval we construct a measure of independence for the components of the pairs. We define distance covariance and distance correlation based on approximations of the component processes ... More
Basic invariants and reciprocity theorems for the Hopf monoid of hypergraphs and its sub-monoidsJun 22 2018Nov 20 2018In arXiv:1709.07504 Ardila and Aguiar give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, we define in this paper a new polynomial invariant on hypergraphs. We give ... More
Linear systems on semisimple Lie groups: the solution, stability, conjugacy, and an application on the 3-dimensional caseJun 21 2018Our main is to study linear systems on real, connected, semisimple Lie groups. We present the solution of linear systems and from this, we work with stability at the origin and construct a conjugacy by homomorphism of ones. Furthermore, we explicit solutions ... More
On order continuous duals of vector lattices of continuous functions on resolvable spacesJun 19 2018A topological space $X$ is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that the order continuous dual of a vector lattice of (not necessarily bounded) continuous functions on a resolvable ... More
Ansatz for $(-1)^{n-1}\nabla p_n$Jun 14 2018Aug 16 2018We construct a special family of equivariant coherent sheaves on the Hilbert scheme on $n$-points in the affine plane. The equivariant Euler characteristic of these sheaves are closely related to the symmetic functions $(-1)^{n-1} \nabla p_n$. We prove ... More
Approximation of BV by SBV functions in metric spacesJun 12 2018In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special functions of ... More
Exact computation over topological spacesJun 02 2018We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real computation (see [Bauer&Kavkler2008] ... More
Asynchronous Batch and PIR Codes from HypergraphsJun 02 2018Sep 16 2018We propose a new model of asynchronous batch codes that allow for parallel recovery of information symbols from a coded database in an asynchronous manner, i.e. when different queries take different time to process. Then, we show that the graph-based ... More
A stronger reformulation of Webb's conjecture in terms of finite topological spacesMay 23 2018We investigate a stronger formulation of Webb's conjecture on the contractibilty of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more recently, by Bux, ... More