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Online Sampling from Log-Concave DistributionsFeb 21 2019Given a sequence of convex functions $f_0, f_1, \ldots, f_T$, we study the problem of sampling from the Gibbs distribution $\pi_t \propto e^{-\sum_{k=0}^t f_k}$ for each epoch $t$ in an online manner. This problem occurs in applications to machine learning, ... More
On the growth rate of chromatic numbers of finite subgraphsFeb 21 2019We prove that, for every function $f:\mathbb{N} \rightarrow \mathbb{N}$, there is a graph $G$ with uncountable chromatic number such that, for every $k \in \mathbb{N}$ with $k \geq 3$, every subgraph of $G$ with fewer than $f(k)$ vertices has chromatic ... More
Coloring squares of graphs with mad constraintsFeb 21 2019A proper vertex $k$-coloring of a graph $G=(V,E)$ is an assignment $c:V\to \{1,2,\ldots,k\}$ of colors to the vertices of the graph such that no two adjacent vertices are associated with the same color. The square $G^2$ of a graph $G$ is the graph defined ... More
Reconfiguration Graph for Vertex Colourings of Weakly Chordal GraphsFeb 21 2019The reconfiguration graph $R_k(G)$ of the $k$-colourings of a graph $G$ contains as its vertex set the $k$-colourings of $G$ and two colourings are joined by an edge if they differ in colour on just one vertex of $G$. We answer a question of Bonamy, Johnson, ... More
The diagonal of the associahedraFeb 21 2019This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplices and the cubes and we solve it for the associahedra, also known as Stasheff ... More
Integer Linear Programming Formulations for Double Roman Domination ProblemFeb 21 2019For a graph $G= (V,E)$, a double Roman dominating function (DRDF) is a function $f : V \to \{0,1,2,3\}$ having the property that if $f (v) = 0$, then vertex $v$ must have at least two neighbors assigned $2$ under $f$ or one neighbor $u$ with $f (u) = ... More
On the existence of dense substructures in finite groupsFeb 21 2019Fix $k \geq 6$. We prove that any large enough finite group $G$ contains $k$ elements which span quadratically many triples of the form $(a,b,ab) \in S \times G$, given any dense set $S \subseteq G \times G$. The quadratic bound is asymptotically optimal. ... More
Sums of linear transformations in higher dimensionsFeb 20 2019In this paper, we prove the following two results. Let $d$ be a natural number and $q,s$ be co-prime integers such that $1 \leq |s| < |q|$. Then there exists a constant $\delta > 0$ depending only on $q,s$ and $d$ such that for any finite subset $A$ of ... More
On completely regular and completely transitive codes derived from Hamming codesFeb 20 2019Given a parity-check matrix $H_m$ of a $q$-ary Hamming code, we consider a partition of the columns into two subsets. Then, we consider the two codes that have these submatrices as parity-check matrices. We obtain that if one of these codes is a Hamming ... More
An observation on the determinant of a Sylvester-Kac type matrixFeb 20 2019Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.
Proof of the Brown-Erdős-Sós conjecture in groupsFeb 20 2019The conjecture of Brown, Erd\H{o}s and S\'os from 1973 states that, for any $k \ge 3$, if a $3$-uniform hypergraph $H$ with $n$ vertices does not contain a set of $k+3$ vertices spanning at least $k$ edges then it has $o(n^2)$ edges. The case $k=3$ of ... More
Fourier and Circulant Matrices are Not RigidFeb 19 2019The concept of matrix rigidity was first introduced by Valiant in [Val77]. Roughly speaking, a matrix is rigid if its rank cannot be reduced significantly by changing a small number of entries. There has been extensive interest in rigid matrices as Valiant ... More
Characteristic elements for real hyperplane arrangementsFeb 19 2019Characteristic elements of the Tits algebra of a real hyperplane arrangement carry information about the characteristic polynomial. We present this notion and its basic properties, and apply it to derive various results about the characteristic polynomial ... More
Minuscule doppelgängers, the coincidental down-degree expectations property, and rowmotionFeb 19 2019We relate Reiner, Tenner, and Yong's coincidental down-degree expectations (CDE) property of posets to the minuscule doppelg\"{a}nger pairs studied by Hamaker, Patrias, Pechenik, and Williams. Via this relation, we put forward a series of conjectures ... More
Stability in a groupFeb 19 2019We develop local stable group theory directly from topological dynamics, and extend the main results in this subject to the setting of stability "in a model". Specifically, given a group $G$, we analyze the structure of sets $A\subseteq G$ such that the ... More
Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curvesFeb 19 2019We define a symmetric monoidal category Trop which, roughly, has degrees of tropical curves as its objects and types of tropical curves as its morphisms. A symmetric monoidal functor with domain Trop is what we call a (2D) tropical quantum field theory ... More
Cubillages of cyclic zonotopesFeb 19 2019This paper (written in Russian) presents a survey of new and earlier results on fine zonotopal tilings (briefly, cubillages) of cyclic zonotopes. The combinatorial theory of these objects is of interest in its own right and also has a connection to higher ... More
On the bi-Lipschitz geometry of lamplighter graphsFeb 19 2019In this article we start a systematic study of the bi-Lipschitz geometry of lamplighter graphs. We prove that lamplighter graphs over trees bi-Lipschitzly embed into Hamming cubes with distortion at most $6$. It follows that lamplighter graphs over countable ... More
List Ramsey numbersFeb 19 2019We introduce the list colouring extension of classical Ramsey numbers. We investigate when the two Ramsey numbers are equal, and in general, how far apart they can be from each other. We find graph sequences where the two are equal and where they are ... More
Lickorish type construction of manifolds over simple polytopesFeb 19 2019This paper is a survey on the Lickorish type construction of some kind of closed manifolds over simple convex polytopes. Inspired by Lickorish's theorem, we propose a method to describe certain families of manifolds over simple convex polytopes with torus ... More
Moderate deviations of subgraph counts in the Erdős-Rényi random graphs $G(n,m)$ and $G(n,p)$Feb 18 2019The main contribution of this article is an asymptotic expression for the rate associated with moderate deviations of subgraph counts in the Erd\H{o}s-R\'enyi random graph $G(n,m)$. Our approach is based on applying Freedman's inequalities for the probability ... More
Characterizing the Integrality Gap of the Subtour LP for the Circulant Traveling Salesman ProblemFeb 18 2019We consider the integrality gap of the subtour LP relaxation of the Traveling Salesman Problem restricted to circulant instances. De Klerk and Dobre conjectured that the value of the optimal solution to the subtour LP on these instances is equal to an ... More
On a theorem of Baxter and Zeilberger via a result of RoselleFeb 18 2019We provide a new proof of a result of Baxter and Zeilberger showing that inv and maj on permutations are jointly independently asymptotically normally distributed. The main feature of our argument is that it uses a generating function due to Roselle, ... More
Asymptotic Hecke algebras and Lusztig-Vogan bijection via affine matrix-ball constructionFeb 18 2019Affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of Robinson-Schensted correspondence. We show that AMBC gives a simple way to compute a distinguished (or Duflo) involution ... More
A Cheeger inequality for graphs based on a reflection principleFeb 18 2019Given a graph with a designated set of boundary vertices, we define a new notion of a Neumann Laplace operator on a graph using a reflection principle. We show that the first eigenvalue of this Neumann graph Laplacian satisfies a Cheeger inequality.
A Combinatorial Identity for Rooted Labelled ForestsFeb 18 2019In this brief note a purely combinatorial proof for an identity related to rooted forests and unordered set partitions is provided. Furthermore, references that put this type of identity in the context of forest volumes are given.
Optimal Scaling and Shaping of Random Walk Metropolis via Diffusion Limits of Block-I.I.D. TargetsFeb 18 2019This work extends Roberts et al. (1997) by considering limits of Random Walk Metropolis (RWM) applied to block IID target distributions, with corresponding block-independent proposals. The extension verifies the robustness of the optimal scaling heuristic, ... More
Matroid connectivity and singularities of configuration hypersurfacesFeb 18 2019Consider a linear realization of a matroid over a field. One associates to it a configuration polynomial and bilinear form with polynomial coefficients. The corresponding configuration hypersurface and its non-smooth locus support the respective first ... More
Find Subtrees of Specified Weight and Cycles of Specified Length in Linear TimeFeb 18 2019We introduce a variant of DFS which finds subtrees of specified weight in linear time, by which, as observed by Mohr, cycles of specified length in planar hamiltonian graphs can be found. We show, for example, that every planar hamiltonian graph $G$ with ... More
The Arctic curve for Aztec rectangles with defects via the Tangent MethodFeb 18 2019The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated Non-Intersecting Lattice Path configurations are ... More
Information-theoretic lower bounds for quantum sortingFeb 18 2019We analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set $P$ and are asked to identify a linear extension of $P$ using pairwise comparisons. For the standard sorting problem, in ... More
Hamiltonicity of bi-power of bipartite graphs, for finite and infinite casesFeb 18 2019For a graph $G$, the $t$-th power $G^t$ is the graph on $V(G)$ such that two vertices are adjacent if and only if they have distance at most $t$ in $G$; and the $t$-th bi-power $G_B^t$ is the graph on $V(G)$ such that two vertices are adjacent if and ... More
Hamiltonian circles of the prism of infinite cubic graphsFeb 18 2019A circle of a infinite locally finite graph $G$ is a homeomorphic mapping of the unit circle $S^1$ in $|G|$, the Freudenthal compactification of $G$. A circle of $G$ is Hamiltonian if it meets every vertex (and then every end) of $G$. Paulraja proved ... More
A Generalization of the "Raboter" OperationFeb 17 2019We generalize an operation described by Sloane on the binary representation of an integer to other bases, thus finding several new sequences.
Braces of Perfect Matching Width 2Feb 17 2019A graph G is called matching covered if it is connected and every edge is contained in a perfect matching. Perfect matching width is a width parameter for matching covered graphs based on a branch decomposition that can be considered a generalisation ... More
On the additive period length of the Sprague-Grundy function of certain Nim-like gamesFeb 17 2019We examine the structure of the additive period of the Sprague-Grundy function of Nim-like games, among them Wythoff's Game, and deduce a bound for the length of the period and preperiod.
$3$-uniform hypergraphs without a cycle of length fiveFeb 17 2019In this paper we show that the maximum number of hyperedges in a $3$-uniform hypergraph on $n$ vertices without a (Berge) cycle of length five is less than $(0.254 + o(1))n^{3/2}$, improving an estimate of Bollob\'as and Gy\H{o}ri. We obtain this result ... More
Double coverings of arrangement complements and $2$-torsion in Milnor fiber homologyFeb 17 2019We prove that mod $2$ Betti numbers of the double covering of a complex hyperplane arrangement complement is combinatorially determined. The proof is based on a relation between mod $2$ Aomoto complex and the transfer long exact sequence. Applying the ... More
Enumerative combinatorics on determinants and signed bigrassmannian polynomialsFeb 17 2019As an application of linear algebra for enumerative combinatorics, we introduce two new ideas, signed bigrassmannian polynomials and bigrassmannian determinant. First, a signed bigrassmannian polynomial is a variant of the statistic given by the number ... More
Lagrangian densities of short 3-uniform linear paths and Turán numbers of their extensionsFeb 17 2019For a fixed positive integer $n$ and an $r$-uniform hypergraph $H$, the Tur\'an number $ex(n,H)$ is the maximum number of edges in an $H$-free $r$-uniform hypergraph on $n$ vertices, and the Lagrangian density of $H$ is defined as $\pi_{\lambda}(H)=\sup ... More
Enumerating Unique Computational Graphs via an Iterative Graph InvariantFeb 17 2019In this report, we describe a novel graph invariant for computational graphs (colored directed acylic graphs) and how we used it to generate all distinct computational graphs up to isomorphism for small graphs. The algorithm iteratively applies isomorphism-invariant ... More
Finding any given 2-factor in sparse pseudorandom graphs efficientlyFeb 16 2019Given an $n$-vertex pseudorandom graph $G$ and an $n$-vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, i.e.\ an embedding $\varphi\colon V(H)\to V(G)$ so that $\varphi(u)\varphi(v)\in E(G)$ for all $uv\in E(H)$. ... More
Chordal graphs are easily testableFeb 16 2019We prove that the class of chordal graphs is easily testable in the following sense. There exists a constant $c>0$ such that, if adding/removing at most $\epsilon n^2$ edges to a graph $G$ with $n$ vertices does not make it chordal, then a set of $(1/\epsilon)^c$ ... More
A simple proof of a congruence for a series involving the little $q$-Jacobi polynomialsFeb 16 2019We give a simple and a more explicit proof of a mod $4$ congruence for a series involving the little $q$-Jacobi polynomials which arose in a recent study of a certain restricted overpartition function.
Flip distances between graph orientationsFeb 16 2019Flip graphs are a ubiquitous class of graphs, which encode relations induced on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance, are the graphs induced by quadrilateral flips in triangulations of a ... More
Questions on the Structure of Perfect Matchings inspired by Quantum PhysicsFeb 16 2019We state a number of related questions on the structure of perfect matchings. Those questions are inspired by and directly connected to Quantum Physics. In particular, they concern the constructability of general quantum states using modern photonic technology. ... More
Survey of Cubic Fibonacci Identities - When Cuboids Carry WeightFeb 15 2019The aim of this paper is to present a comprehensive survey of cubic Fibonacci identities, trying to uncover as many as possible. From the outset, our rationale for a very careful search on an apparently obscure problem was not only a matter of mathematical ... More
Jacobi Sums and Correlations of Sidelnikov SequencesFeb 15 2019We consider the problem of determining the cross-correlation values of the sequences in the families comprised of constant multiples of $M$-ary Sidelnikov sequences over $\mathbb{F}_q$, where $q$ is a power of an odd prime $p$. We show that the cross-correlation ... More
Universally Sparse Hypergraphs with Applications to Coding TheoryFeb 15 2019For fixed integers $r\ge 2,e\ge 2,v\ge r+1$, an $r$-uniform hypergraph is called $\mathscr{G}_r(v,e)$-free if the union of any $e$ distinct edges contains at least $v+1$ vertices. Let $f_r(n,v,e)$ denote the maximum number of edges in a $\mathscr{G}_r(v,e)$-free ... More
Numerical and Symbolic Studies of the Peaceable Queens ProblemFeb 15 2019We discuss, and make partial progress on, the peaceable queens problem, the protagonist of OEIS sequence A250000. Symbolically, we prove that Jubin's construction of two pentagons is at least a local optimum. Numerically, we find the exact numerical optimums ... More
Minimum degree conditions for monochromatic cycle partitioningFeb 15 2019Feb 18 2019A classical result of Erd\H{o}s, Gy\'arf\'as and Pyber states that any $r$-edge-coloured complete graph has a partition into $O(r^2 \log r)$ monochromatic cycles. Here we determine the minimum degree threshold for this property. More precisely, we show ... More
Beyond Coins, Stamps, and Chicken McNuggets: an Invitation to Numerical SemigroupsFeb 15 2019We give a self contained introduction to numerical semigroups, and present several open problems centered on their factorization properties.
On the number of hinges defined by a point set in $\mathbb R^2$Feb 15 2019This note strengthens, modulo a $\log n$ factor, the Guth-Katz estimate for the number of pair-wise incidences of lines in $\mathbb R^3$, arising in the context of the plane Erd\"os distinct distance problem to a second moment bound. This enables one ... More
On semilinear sets and asymptotically approximate groupsFeb 15 2019Let $G$ be any group and $A$ be an arbitrary subset of $G$ (not necessarily symmetric and not necessarily containing the identity). The $h$-fold product set of $A$ is defined as $$A^{h} :=\lbrace a_{1}.a_{2}...a_{h} : a_{1},\ldots,a_n \in A \rbrace.$$ ... More
On a conjecture of Bondy and VinceFeb 15 2019Twenty years ago Bondy and Vince conjectured that for any nonnegative integer $k$, except finitely many counterexamples, every graph with $k$ vertices of degree less than three contains two cycles whose lengths differ by one or two. The case $k\leq 2$ ... More
Complexity of the circulant foliation over a graphFeb 15 2019In the present paper, we investigate the complexity of infinite family of graphs $H_n=H_n(G_1,\,G_2,\ldots,G_m)$ obtained as a circulant foliation over a graph $H$ on $m$ vertices with fibers $G_{1},\,G_{2},\ldots,G_{m}.$ Each fiber $G_{i}=C_{n}(s_{i,1},\,s_{i,2},\ldots,s_{i,k_{i}})$ ... More
There are at most $2^{d+1}-2$ neighbourly simplices in dimension $d$Feb 14 2019A combinatorial theorem on families of disjoint sub-boxes of a discrete cube, which implies that there at most $2^{d+1}-2$ neighbourly simplices in $\mathbb R^d$, is presented.
Quantifier alternation in a class of recursively defined tree propertiesFeb 14 2019Alternating quantifier depth is a natural measure of difficulty required to express first order logical sentences. We define a sequence of first order properties on rooted, locally finite trees in a recursive manner, and provide rigorous arguments for ... 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
A tour problem on a toroidal boardFeb 14 2019Let $A$ be an $n\times m$ toroidal array consisting of filled cells and empty cells. Assume that an orientation $R=(r_1,\dots,r_n)$ of each row and $C=(c_1,\dots,c_m)$ of each column of $A$ is fixed. Given an initial filled cell $(i_1,j_1)$ consider the ... More
On L(2,1)-labelings of oriented graphsFeb 14 2019We extend a result of Griggs and Yeh about the maximum possible value of the L(2,1)-labeling number of a graph in terms of its maximum degree to oriented graphs. We consider the problem both in the usual definition of the oriented L(2,1)-labeling number ... More
Prescribing Symmetries and Automorphisms for PolytopesFeb 14 2019We study the groups for which it is possible to find a convex polytope with that group as automorphism group with additional geometric conditions on the action of the group or its subgroups. In particular, we prove that for every abelian group G of even ... More
The simple graph threshold number $σ(r,s,a,t)$Feb 14 2019For $d \ge 1$, $s \ge 0$ a $(d, d+s)$-{\em graph} is a graph whose degrees all lie in the interval $\{d, d+1, \ldots, d + s\}$. For $r \ge 1$, $a \ge 0$, an $(r, r+a)$-{\em factor} of a graph $G$ is a spanning $(r, r+a)$-subgraph of $G$. An $(r, r+a)$-{\em ... More
Subgaussianity is hereditarily determinedFeb 14 2019Let $n$ be a positive integer, let $\boldsymbol{X}=(X_1,\dots,X_n)$ be a random vector in $\mathbb{R}^n$ with bounded entries, and let $(\theta_1,\dots,\theta_n)$ be a vector in $\mathbb{R}^n$. We show that the subgaussian behavior of the random variable ... More
Sequentially Cohen-Macaulay matroidal idealsFeb 14 2019Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all sequentially Cohen-Macaulay ... More
Sequentially Cohen-Macaulay matroidal idealsFeb 14 2019Feb 17 2019Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all sequentially Cohen-Macaulay ... More
A note on rainbow saturation number of pathsFeb 14 2019For a fixed graph $F$ and an integer $t$, the rainbow saturation number of $F$, denoted by $sat_t(n,\mathfrak{R}(F))$, is defined as the minimum number of edges in a $t$-edge-colored graph on $n$ vertices which does not contain a rainbow copy of $F$, ... More
A note on rainbow saturation number of pathsFeb 14 2019Feb 18 2019For a fixed graph $F$ and an integer $t$, the rainbow saturation number of $F$, denoted by $sat_t(n,\mathfrak{R}(F))$, is defined as the minimum number of edges in a $t$-edge-colored graph on $n$ vertices which does not contain a rainbow copy of $F$, ... More
Searching for modular companionsFeb 14 2019In this note, we report on the results of a computer search performed to find possible modular companions to certain $q$-series identities and conjectures. For the search, we use conditions arising from the asymptotics of Nahm sums. We focus on two sets ... More
Unique Differences in Symmetric Subsets of $\mathbb{F}_p$Feb 14 2019Let $p$ be a prime and let $A$ be a subset of $\mathbb{F}_p$ with $A=-A$ and $|A\setminus\{0\}| \leq 2\log_3(p)$. Then there is an element of $\mathbb{F}_p$ which has a unique representation as a difference of two elements of $A$.
Covering random graphs by monochromatic trees and Helly-type results for hypergraphsFeb 13 2019Feb 19 2019How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given $r$-edge-coloured graph $G$? These problems were introduced in the 1960's and were intensively studied by various researchers over the last 50 years. ... More
Covering random graphs by monochromatic trees and Helly-type results for hypergraphsFeb 13 2019How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given $r$-edge-coloured graph $G$? These problems were introduced in the 1960's and were intensively studied by various researchers over the last 50 years. ... More
Embeddings of Orlicz-Lorentz spaces into $L_1$Feb 13 2019In this article, we show that Orlicz-Lorentz spaces $\ell^n_{M,a}$, $n\in\mathbb N$ with Orlicz function $M$ and weight sequence $a$ are uniformly isomorphic to subspaces of $L_1$ if the norm $\|\cdot\|_{M,a}$ satisfies certain Hardy-type inequalities. ... More
Correspondence functors and latticesFeb 13 2019A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated to any finite ... More
Sufficient conditions for a digraph to admit a $(1,\leq\ell)$-identifying codeFeb 13 2019A $(1,\le \ell)$-identifying code in a digraph $D$ is a subset $C$ of vertices of $D$ such that all distinct subsets of vertices of cardinality at most $\ell$ have different closed in-neighborhoods within $C$. In this paper, we give some sufficient conditions ... More
Topological dynamics of Polish group extensionsFeb 13 2019We consider a short exact sequence $1\to H\to G\to K\to 1$ of Polish groups and consider what can be deduced about the dynamics of $G$ given information about the dynamics of $H$ and $K$. We prove that if the respective universal minimal flows $M(H)$ ... More
Correspondence functors and finiteness conditionsFeb 13 2019We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties ... More
Local approximation of the Maximum Cut in regular graphsFeb 13 2019This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communication ... More
Surface Words are Determined by Word Measures on GroupsFeb 13 2019Every word $w$ in a free group naturally induces a probability measure on every compact group $G$. For example, if $w=\left[x,y\right]$ is the commutator word, a random element sampled by the $w$-measure is given by the commutator $\left[g,h\right]$ of ... More
On the achromatic number of signed graphsFeb 13 2019In this paper, we generalize the concept of complete coloring and achromatic number to 2-edge-colored graphs and signed graphs. We give some useful relationships between different possible definitions of such achromatic numbers and prove that computing ... More
The algebra of Boolean matrices, correspondence functors, and simplicityFeb 13 2019We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ... More
k-Dismantlability in GraphsFeb 12 2019Given a finite undirected graph $X$, a vertex is $0$-dismantlable if its open neighborhood is a cone and $X$ is $0$-dismantlable if it is reducible to a single vertex by successive deletions of $0$-dismantlable vertices. By an iterative process, a vertex ... More
Optimal BIBD-extended designsFeb 12 2019Balanced incomplete block designs (BIBDs) are a class of designs with v treatments and b blocks of size k that are optimal with regards to a wide range of optimality criteria, but it is not clear which designs to choose for combinations of v, b and k ... More
A partial theta function Borwein conjectureFeb 12 2019We present an infinite family of Borwein type $+ - - $ conjectures. The expressions in the conjecture are related to multiple basic hypergeometric series with Macdonald polynomial argument.
On Conflict Free DNA CodesFeb 12 2019DNA storage has emerged as an important area of research. The reliability of DNA storage system depends on designing the DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy a special constraint. ... More
List edge coloring of outer-1-planar graphsFeb 12 2019A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. It is known that the list edge chromatic number $\chi'_l(G)$ of any outer-1-planar graph $G$ with maximum degree ... More
The least H-eigenvalue of signless Laplacian of non-odd-bipartite hypergraphsFeb 12 2019Let $G$ be a connected non-odd-bipartite hypergraph with even uniformity. The least H-eigenvalue of the signless Laplacian tensor of $G$ is simply called the least eigenvalue of $G$ and the corresponding H-eigenvectors are called the first eigenvectors ... More
How to count the number of zeros that a polynomial has on the unit circle?Feb 12 2019The classical problem of counting the number of real zeros of a real polynomial was solved a long time ago by Sturm. The analogous problem of counting the number of zeros that a polynomial has on the unit circle is, however, still an open problem. In ... More
Graver Bases via Quantum Annealing with Application to Non-Linear Integer ProgramsFeb 12 2019We propose a novel hybrid quantum-classical approach to calculate Graver bases, which have the potential to solve a variety of hard linear and non-linear integer programs, as they form a test set (optimality certificate) with very appealing properties. ... More
Bivariate fluctuations for the number of arithmetic progressions in random setsFeb 11 2019We study arithmetic progressions $\{a,a+b,a+2b,\dots,a+(\ell-1) b\}$, with $\ell\ge 3$, in random subsets of the initial segment of natural numbers $[n]:=\{1,2,\dots, n\}$. Given $p\in[0,1]$ we denote by $[n]_p$ the random subset of $[n]$ which includes ... More
A lower bound on permutation codes of distance $n-1$Feb 11 2019A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length $n$ and minimum distance $n-1$. When such codes of length $p+1$ are included as ingredients, we ... More
The Iris function and the matrix permanentFeb 11 2019This paper defines the Iris function and provides two formulations of the matrix permanent. The first formulation, valid for arbitrary complex matrices, expresses the permanent of a complex matrix as a contour integral of a second order Iris function ... More
On the number of pancake stacks requiring 4 flips to be sortedFeb 11 2019Using an existing classification results for the 7- and 8-cycles in the pancake graph, we determine the number of permutations that require 4 pancake flips (prefix reversals) to be sorted. A similar characterization of the 8-cycles in the burnt pancake ... More
Limit theory for the number of isolated and extreme points in hyperbolic random geometric graphsFeb 11 2019Given $\alpha \in (0, \infty)$ and $r \in (0, \infty)$, let ${\cal D}_{r, \alpha}$be the disc of radius $r$ in the hyperbolic plane having curvature $-\alpha^2$. Consider the Poisson point process having uniform intensity density on ${\cal D}_{R, \alpha}$, ... 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
All those EPPA classes (Strengthenings of the Herwig-Lascar theorem)Feb 11 2019In this paper we prove a general theorem showing the extension property for partial automorphisms (EPPA, also called the Hrushovski property) for classes of structures containing relations and unary functions, optionally equipped with a permutation group ... More
Congruences on sums of $q$-binomial coefficientsFeb 11 2019We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by Guo. We also ... More
A Sundaram type bijection for $\mathrm{SO}(2k+1)$: vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableauFeb 11 2019We present a bijection between vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau for the special orthogonal group $\mathrm{SO}(2k+1)$. This bijection is motivated by the direct-sum-decomposition ... More
Weighted prime geodesic theoremsFeb 11 2019Prime geodesic theorems for weighted infinite graphs and weighted building quotients are given. The growth rates are expressed in terms of the spectral data of suitable translation operators inspired by a paper of Bass.
Flexibility of planar graphs of girth at least sixFeb 11 2019Let G be a planar graph with a list assignment L. Suppose a preferred color is given for some of the vertices. We prove that if G has girth at least six and all lists have size at least three, then there exists an L-coloring respecting at least a constant ... More