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Explicit upper bounds for the Stirling numbers of the first kind J. Comb. Theory A (IF 1.263) Pub Date : 20220811
José A. AdellWe give explicit upper bounds for the Stirling numbers of the first kind s(n,m) which are asymptotically sharp. The form of such bounds varies according to m lying in the central or noncentral regions of {1,…,n}. In each case, we use a different probabilistic representation of s(n,m) in terms of well known random variables to show the corresponding upper bounds. Some applications concerning the Riemann

On a construction by Giudici and Parker on commuting graphs of groups J. Comb. Theory A (IF 1.263) Pub Date : 20220727
Giovanni CutoloGiven a connected graph Δ, a group G can be constructed in such a way that Δ is often isomorphic to a subgraph of the commuting graph KG(Δ) of G. We show that, with one exception, KG(Δ) is connected, and in this latter case its diameter is at most that of Δ. If Δ is a path of length n>2, then diam(KG(Δ))=n.

KazhdanLusztig polynomials of fan matroids, wheel matroids, and whirl matroids J. Comb. Theory A (IF 1.263) Pub Date : 20220727
Linyuan Lu, Matthew H.Y. Xie, Arthur L.B. YangThe KazhdanLusztig polynomial of a matroid was introduced by Elias, Proudfoot and Wakefield. The properties of these polynomials need to be further explored. In this paper we prove that the KazhdanLusztig polynomials of fan matroids coincide with Motzkin polynomials, which was conjectured by Gedeon. As a byproduct, we determine the KazhdanLusztig polynomials of graphic matroids of squares of paths

Van Lint–MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields J. Comb. Theory A (IF 1.263) Pub Date : 20220725
Shamil Asgarli, Chi Hoi YipA wellknown conjecture due to van Lint and MacWilliams states that if A is a subset of Fq2 such that 0,1∈A, A=q, and a−b is a square for each a,b∈A, then A must be the subfield Fq. This conjecture is often phrased in terms of the maximum cliques in Paley graphs. It was first proved by Blokhuis and later extended by Sziklai to generalized Paley graphs. In this paper, we give a new proof of the conjecture

Infinite families of optimal systems of biangular lines related to representations of SL(2,Fq) J. Comb. Theory A (IF 1.263) Pub Date : 20220719
Mikhail GanzhinovA line packing is optimal if its coherence is as small as possible. Most interesting examples of optimal line packings are achieving equality in some of the known lower bounds for coherence. In this paper two infinite families of real and complex biangular line packings are presented. New packings achieve equality in the real or complex second Levenshtein bound respectively. Both infinite families

Linear cutting blocking sets and minimal codes in the rank metric J. Comb. Theory A (IF 1.263) Pub Date : 20220719
Gianira N. Alfarano, Martino Borello, Alessandro Neri, Alberto RavagnaniThis work investigates the structure of rankmetric codes in connection with concepts from finite geometry, most notably the qanalogues of projective systems and blocking sets. We also illustrate how to associate a classical Hammingmetric code to a rankmetric one, in such a way that various rankmetric properties naturally translate into the homonymous Hammingmetric notions under this correspondence

An algebraic approach to ErdősKoRado sets of flags in spherical buildings J. Comb. Theory A (IF 1.263) Pub Date : 20220711
Jan De Beule, Sam Mattheus, Klaus MetschIn this paper, oppositeness in spherical buildings is used to define an EKRproblem for flags in projective and polar spaces. A novel application of the theory of buildings and IwahoriHecke algebras is developed to prove sharp upper bounds for EKRsets of flags. In this framework, we can reprove and generalize previous upper bounds for EKRproblems in projective and polar spaces. The bounds are obtained


Covers of complete graphs and related association schemes J. Comb. Theory A (IF 1.263) Pub Date : 20220620
Ludmila Yu. TsiovkinaWe investigate the association schemes Inv(G) that are formed by the collection of orbitals of a permutation group G, for which the (underlying) graph Γ of a basis relation is a distanceregular antipodal cover of the complete graph. The group G can be regarded as an edgetransitive group of automorphisms of Γ and induces a 2homogeneous permutation group on the set of its antipodal classes, which

Planarity can be verified by an approximate proof labeling scheme in constanttime J. Comb. Theory A (IF 1.263) Pub Date : 20220610
Gábor ElekApproximate proof labeling schemes were introduced by CensorHillel, Paz and Perry [3]. Roughly speaking, a graph property P can be verified by an approximate proof labeling scheme in constanttime if the vertices of a graph having the property can be convinced, in a short period of time not depending on the size of the graph, that they are having the property P or at least they are not far from being

ErdősKoRado sets of flags of finite sets J. Comb. Theory A (IF 1.263) Pub Date : 20220610
Klaus MetschA flag of a finite set S is a set f of nonempty proper subsets of S such that A⊆B or B⊆A for all A,B∈f. The set {A:A∈f} is called the type of f. Two flags f and f′ are in general position (with respect to S) when A∩B=∅ or A∪B=S for all A∈f and B∈f′. We study sets of flags of a fixed type T that are mutually not in general position and are interested in the largest cardinality of these sets. This

On the denominators of Young's seminormal basis J. Comb. Theory A (IF 1.263) Pub Date : 20220609
Steen RyomHansenWe study the seminormal basis {ft} for the Specht modules of the IwahoriHecke algebra Hn(q) of type An−1. We focus on the base change coefficients between the seminormal basis {ft} and Murphys' standard basis {xt} with emphasis on the denominators of these coefficients. In certain important cases we obtain simple formulas for these coefficients involving hook lengths. Even for general standard tableaux

The Pieri formulas for hook type Schur multiple zeta functions J. Comb. Theory A (IF 1.263) Pub Date : 20220609
Maki Nakasuji, Wataru TakedaWe study the Pieri type formulas for the Schur multiple zeta functions along with those for the Schur functions. To express these formulas, we introduce a new insertion rule for adding boxes in the Young tableaux and obtain the results for the hook type Schur multiple zeta functions. For the proof, we show certain extended JacobiTrudi formulas for the Schur multiple zeta functions.

A decomposition of ballot permutations, pattern avoidance and Gessel walks J. Comb. Theory A (IF 1.263) Pub Date : 20220603
Zhicong Lin, David G.L. Wang, Tongyuan ZhaoA permutation whose any prefix has no more descents than ascents is called a ballot permutation. In this paper, we present a decomposition of ballot permutations that enables us to construct a bijection between ballot permutations and odd order permutations, which proves a setvalued extension of a conjecture due to Spiro using the statistic of peak values. This bijection also preserves the neighbors

Beyond Göllnitz' theorem II: Arbitrarily many primary colors J. Comb. Theory A (IF 1.263) Pub Date : 20220603
Isaac KonanIn 2003, Alladi, Andrews and Berkovich proved a four parameter partition identity lying beyond a celebrated identity of Göllnitz. Since then it has been an open problem to extend their work to five or more parameters. In part I of this pair of papers, we took a first step in this direction by giving a bijective proof of a reformulation of their result. We introduced forbidden patterns, bijectively

Generalized polygons and star graphs of cyclic presentations of groups J. Comb. Theory A (IF 1.263) Pub Date : 20220523
Ihechukwu Chinyere, Gerald WilliamsGroups defined by presentations for which the components of the corresponding star graph are the incidence graphs of generalized polygons are of interest as they are small cancellation groups that – via results of Edjvet and Vdovina – are fundamental groups of polyhedra with the generalized polygons as links and so act on Euclidean or hyperbolic buildings; in the hyperbolic case the groups are SQuniversal

Symmetries in graphs via simplicial automorphisms J. Comb. Theory A (IF 1.263) Pub Date : 20220519
Klavdija Kutnar, Dragan MarušičAn automorphism ρ of a graph X is said to be semiregular provided all of its cycles in its cycle decomposition are of the same length, and is said to be simplicial if it is semiregular and the quotient multigraph Xρ of X with respect to ρ is a simple graph, and thus of the same valency as X. It is shown that, with the exception of the complete graph K4, the Petersen graph, the Coxeter graph and the

Quadratic sets on the Klein quadric J. Comb. Theory A (IF 1.263) Pub Date : 20220506
Bart De BruynConsider the Klein quadric Q+(5,q) in PG(5,q). A set of points of Q+(5,q) is called a quadratic set if it intersects each plane π of Q+(5,q) in a possibly reducible conic of π, i.e. in a singleton, a line, an irreducible conic, a pencil of two lines or the whole of π. A quadratic set is called good if at most two of these possibilities occur as π ranges over all planes of Q+(5,q). We obtain several

Matroids with different configurations and the same Ginvariant J. Comb. Theory A (IF 1.263) Pub Date : 20220506
Joseph E. BoninFrom the configuration of a matroid (which records the size and rank of the cyclic flats and the containments among them, but not the sets), one can compute several muchstudied matroid invariants, including the Tutte polynomial and a newer, stronger invariant, the Ginvariant. To gauge how much additional information the configuration contains compared to these invariants, it is of interest to have

Generalized Frobenius partitions, Motzkin paths, and Jacobi forms J. Comb. Theory A (IF 1.263) Pub Date : 20220502
Yuze Jiang, Larry Rolen, Michael WoodburyWe show how Andrews' generating functions for generalized Frobenius partitions can be understood within the theory of Eichler and Zagier as specific coefficients of certain Jacobi forms. This reformulation leads to a recursive process which yields explicit formulas for the generalized Frobenius partition generating functions in terms of infinite qproducts. In particular, we show that specific examples

On cyclic quiver parabolic KostkaShoji polynomials J. Comb. Theory A (IF 1.263) Pub Date : 20220503
Daniel Orr, Mark ShimozonoWe obtain an explicit combinatorial formula for certain parabolic KostkaShoji polynomials associated with the cyclic quiver, generalizing results of Shoji and of Liu and Shoji.

On the orbital diameter of groups of diagonal type J. Comb. Theory A (IF 1.263) Pub Date : 20220503
Kamilla RekvényiThe orbital diameter of a primitive permutation group is the maximal diameter of its orbital graphs. There has been a lot of interest in bounds for the orbital diameter. In this paper we provide explicit bounds on the diameters of groups of simple diagonal type. As a consequence we obtain a classification of simple diagonal groups with orbital diameter less than or equal to 4. As part of this, we classify

Ryser's Theorem for ρLatin rectangles J. Comb. Theory A (IF 1.263) Pub Date : 20220422
Amin BahmanianLet L be an n×n array whose top left r×s subarray is filled with k different symbols, each occurring at most once in each row and at most once in each column. We find necessary and sufficient conditions that ensure the remaining cells of L can be filled such that each symbol occurs at most once in each row and at most once in each column, and each symbol occurs a prescribed number of times in L. The

On the growth of Artin–Tits monoids and the partial theta function J. Comb. Theory A (IF 1.263) Pub Date : 20220407
Ramón Flores, Juan GonzálezMenesesWe present a new procedure to determine the growth function of a homogeneous Garside monoid, with respect to the finite generating set formed by the atoms. In particular, we present a formula for the growth function of each Artin–Tits monoid of spherical type (hence of each braid monoid) with respect to the standard generators, as the inverse of the determinant of a very simple matrix. Using this approach

Lattice paths and (n − 2)stack sortable permutations J. Comb. Theory A (IF 1.263) Pub Date : 20220406
Cindy C.Y. Gu, Larry X.W. WangWe establish a bijection between the (n−2)stack sortable permutations and the labeled lattice paths. Using this bijection, we directly give combinatorial proof for the logconcavity of the numbers of (n−2)stack sortable permutations with k descents. Furthermore, we prove the numbers of (n−2)stack sortable permutations with k descents satisfy interlacing logconcavity. We also consider a conjecture

Characterization of pary functions in terms of association schemes and its applications J. Comb. Theory A (IF 1.263) Pub Date : 20220401
Yansheng Wu,Jong Yoon Hyun,Yoonjin LeeWe obtain an explicit criterion for pary functions to produce association schemes in terms of their Walsh spectrum. Employing this characterization, we explicitly find a correlation between pary bent functions and association schemes; to be more exact, we prove that a pary bent function induces a pclass association scheme if and only if the function is weakly regular. As applications of our main

Comparison between regularity of small symbolic powers and ordinary powers of an edge ideal J. Comb. Theory A (IF 1.263) Pub Date : 20220322
Nguyen Cong Minh, Le Dinh Nam, Thieu Dinh Phong, Phan Thi Thuy, Thanh VuLet I=I(G) be the edge ideal of a simple graph G. We prove thatreg(I(s))=reg(Is) for s=2,3, where I(s) is the sth symbolic power of I. As a consequence, we prove the following boundsregIs≤regI+2s−2, for s=2,3,regI(s)≤regI+2s−2, for s=2,3,4.

Discrete and metric divisorial gonality can be different J. Comb. Theory A (IF 1.263) Pub Date : 20220321
Josse van Dobben de Bruyn, Harry Smit, Marieke van der WegenThis paper compares the divisorial gonality of a finite graph G to the divisorial gonality of the associated metric graph Γ(G,1) with unit lengths. We show that dgon(Γ(G,1)) is equal to the minimal divisorial gonality of all regular subdivisions of G, and we provide a class of graphs for which this number is strictly smaller than the divisorial gonality of G. This settles a conjecture of M. Baker [3

Leray numbers of complexes of graphs with bounded matching number J. Comb. Theory A (IF 1.263) Pub Date : 20220317
Andreas F. Holmsen, Seunghun LeeGiven a graph G on the vertex set V, the nonmatching complex of G, denoted by NMk(G), is the family of subgraphs G′⊂G whose matching number ν(G′) is strictly less than k. As an attempt to extend the result by Linusson, Shareshian and Welker on the homotopy types of NMk(Kn) and NMk(Kr,s) to arbitrary graphs G, we show that (i) NMk(G) is (3k−3)Leray, and (ii) if G is bipartite, then NMk(G) is (2k−2)Leray

Flagtransitive and pointimprimitive symmetric designs with λ ≤ 10 J. Comb. Theory A (IF 1.263) Pub Date : 20220317
Joško Mandić, Aljoša ŠubašićIn a paper published in 2005, Praeger and Zhou improved the upper bound on the number of points of a flagtransitive, pointimprimitive, symmetric design in terms of the number of blocks containing two points. Here we present an improvement of their result, devise a list of feasible parameter sequences for which two points are contained in at most ten blocks, and also develop new methods for the elimination

On a conjecture of the small Davenport constant for finite groups J. Comb. Theory A (IF 1.263) Pub Date : 20220316
Yongke Qu, Yuanlin Li, Daniel TeeuwsenLet G be a multiplicatively written finite group. We denote by d(G) the small Davenport constant of G, that is, the maximal integer ℓ such that there is a sequence of length ℓ over G which has no nontrivial productone subsequence. In 2014, Gao, Li, and Peng conjectured that d(G)≤G/p+p−2 for any finite noncyclic group G, where p is the smallest prime divisor of G. In this paper, we confirm that

On equivalent classes of minimal Abelian codes J. Comb. Theory A (IF 1.263) Pub Date : 20220310
Yuan Ren, Dongchun HanLet Fq be a finite field and G a finite abelian group. An abelian code is an ideal of Fq[G]. Two abelian codes c1 and c2 of Fq[G] are equivalent if there exists an automorphism of G whose linear extension to Fq[G] maps c1 onto c2. MacWilliams determined the number of equivalent classes of minimal abelian codes (minimal ideals) in F2[G] for cyclic group G of odd cardinality. Miller claimed that MacWilliams'

On the Oberwolfach problem for singleflip 2factors via graceful labelings J. Comb. Theory A (IF 1.263) Pub Date : 20220308
A.C. Burgess, P. Danziger, T. TraettaLet F be a 2regular graph of order v. The Oberwolfach problem OP(F), posed in 1967 and still open, asks for a decomposition of Kv into copies of F. In this paper we show that OP(F) has a solution whenever F has a sufficiently large cycle which meets a given lower bound and, in addition, has a singleflip automorphism, which is an involutory automorphism acting as a reflection on exactly one of the

Infinite monochromatic patterns in the integers J. Comb. Theory A (IF 1.263) Pub Date : 20220303
Mauro Di NassoWe show the existence of several infinite monochromatic patterns in the integers obtained as values of suitable symmetric polynomials; in particular, we obtain extensions of both the additive and multiplicative versions of Hindman's theorem. These configurations are obtained by means of suitable symmetric polynomials that mix the two operations. The simplest example is the following. For every finite

Linked partition ideals and the Alladi–Schur theorem J. Comb. Theory A (IF 1.263) Pub Date : 20220303
George E. Andrews, Shane Chern, Zhitai LiLet S denote the set of integer partitions into parts that differ by at least 3, with the added constraint that no two consecutive multiples of 3 occur as parts. We derive trivariate generating functions of Andrews–Gordon type for partitions in S with both the number of parts and the number of even parts counted. In particular, we provide an analytic counterpart of Andrews' recent refinement of the

rfat linearized polynomials over finite fields J. Comb. Theory A (IF 1.263) Pub Date : 20220301
Daniele Bartoli, Giacomo Micheli, Giovanni Zini, Ferdinando Zullorfat polynomials are a natural generalization of scattered polynomials. They define linear sets of the projective line PG(1,qn) of rank n with r points of weight larger than one. Using techniques on algebraic curves and function fields, we obtain numerical bounds for r and the nonexistence of exceptional rfat polynomials with r>0. We completely determine the possible values of r when considering

On the epositivity of trees and spiders J. Comb. Theory A (IF 1.263) Pub Date : 20220225
Kai ZhengWe prove that the chromatic symmetric function of any tree with a vertex of degree at least six is not epositive, that is, it cannot be written as a nonnegative linear combination of elementary symmetric functions. This makes significant progress towards a recent conjecture of Dahlberg, She, and van Willigenburg, who conjectured the result for the chromatic symmetric functions of all trees with a

On the nonexistence of extended 1perfect codes and MDS codes J. Comb. Theory A (IF 1.263) Pub Date : 20220224
Evgeny BespalovWe prove the nonexistence of extended perfect codes in H(n,q), where q=3,4 and n>q+2 or both n and q are odd. In particular, we prove the nonexistence of nonlinear (q+2,qq−1,4)q MDS codes when q is odd.

On npartite digraphical representations of finite groups J. Comb. Theory A (IF 1.263) Pub Date : 20220223
JiaLi Du, YanQuan Feng, Pablo SpigaA group G admits an npartite digraphical representation if there exists a regular npartite digraph Γ such that the automorphism group Aut(Γ) of Γ satisfies the following properties: (1) Aut(Γ) is isomorphic to G, (2) Aut(Γ) acts semiregularly on the vertices of Γ and (3) the orbits of Aut(Γ) on the vertex set of Γ form a partition into n parts giving a structure of npartite digraph to Γ. In this

Fractional meanings of nonrepetitiveness J. Comb. Theory A (IF 1.263) Pub Date : 20220215
Joanna ChybowskaSokół, Michał Dębski, Jarosław Grytczuk, Konstanty JunoszaSzaniawski, Barbara Nayar, Urszula Pastwa, Krzysztof WęsekA sequence S is called rnonrepetitive if no r sequentially adjacent blocks in S are identical. By the classic results of Thue from the beginning of the 20th century, we know that there exist arbitrarily long binary 3nonrepetitive sequences and ternary 2nonrepetitive sequences. This discovery stimulated over the years intensive research leading to various generalizations and many exciting problems

Asymptotic enumeration and distributional properties of galled networks J. Comb. Theory A (IF 1.263) Pub Date : 20220214
Michael Fuchs, GuanRu Yu, Louxin ZhangWe show a firstorder asymptotics result for the number of galled networks with n leaves. This is the first class of phylogenetic networks of large size for which an asymptotic counting result of such strength can be obtained. In addition, we also find the limiting distribution of the number of reticulation nodes of galled networks with n leaves chosen uniformly at random. These results are obtained

Touchard type identity for qNarayana numbers J. Comb. Theory A (IF 1.263) Pub Date : 20220131
Hao PanWe prove a Touchard type identity for qNarayana number as follows:1[n]q[nk]q[nk+1]q=∑h=0min{k,n−1−k}Ch⋅qh2(n−1n−1−h−k,2h,k−h)q, where Ch=1h+1(2hh) is the original Catalan number and (nk0,k1,k2)q is a qanalogue of multinomial coefficient given by∑k0+k1+k2=n(nk0,k1,kn)q⋅q(k22)+(k1+k22)xk1yk2=∏j=0n−1(1+xqj+yq2j).

On symmetric and Hermitian rank distance codes J. Comb. Theory A (IF 1.263) Pub Date : 20220121
Antonio Cossidente, Giuseppe Marino, Francesco PaveseLet M denote the set Sn,q of n×n symmetric matrices with entries in Fq or the set Hn,q2 of n×n Hermitian matrices whose elements are in Fq2. Then M equipped with the rank distance dr is a metric space. We investigate d–codes in (M,dr) and construct d–codes whose sizes are larger than the corresponding additive bounds. In the Hermitian case, we show the existence of an n–code of M, n even and n/2 odd

The Tutte polynomial via lattice point counting J. Comb. Theory A (IF 1.263) Pub Date : 20220117
Amanda Cameron, Alex FinkWe recover the Tutte polynomial of a matroid, up to change of coordinates, from an Ehrhartstyle polynomial counting lattice points in the Minkowski sum of its base polytope and scalings of simplices. Our polynomial has coefficients of alternating sign with a combinatorial interpretation closely tied to the Dawson partition. Our definition extends in a straightforward way to polymatroids, and in this

Beating FredmanKomlós for perfect khashing J. Comb. Theory A (IF 1.263) Pub Date : 20220117
Venkatesan Guruswami, Andrii RiazanovWe say a subset C⊆{1,2,…,k}n is a khash code (also called kseparated) if for every subset of k codewords from C, there exists a coordinate where all these codewords have distinct values. Understanding the largest possible rate (in bits), defined as (log2C)/n, of a khash code is a classical problem. It arises in two equivalent contexts: (i) the smallest size possible for a perfect hash family

Pattern occurrences in kary words revisited: A few new and old observations J. Comb. Theory A (IF 1.263) Pub Date : 20220113
Toufik Mansour, Reza RastegarIn this paper, we study the pattern occurrence in kary words. We prove an explicit upper bound on the number of kary words avoiding any given pattern using a random walk argument. Additionally, we reproduce one already known result on the exponential rate of growth of pattern occurrence in words and establish a simple connection among pattern occurrences in permutations and kary words. A simple

Matchings and squarefree powers of edge ideals J. Comb. Theory A (IF 1.263) Pub Date : 20220111
Nursel Erey, Jürgen Herzog, Takayuki Hibi, Sara Saeedi MadaniSquarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper, we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such powers are linearly related or have linear resolution. We also consider the socalled squarefree Ratliff property.

Incidences between points and curves with almost two degrees of freedom J. Comb. Theory A (IF 1.263) Pub Date : 20220111
Micha Sharir, Noam Solomon, Oleg ZlydenkoWe study incidences between points and (constantdegree algebraic) curves in three dimensions, taken from a family C of curves that have almost two degrees of freedom, meaning that (i) every pair of curves of C intersect in O(1) points, (ii) for any pair of points p, q, there are only O(1) curves of C that pass through both points, and (iii) there exists a 6variate real polynomial F of constant degree

Edgeisoperimetric inequalities and ballnoise stability: Linear programming and probabilistic approaches J. Comb. Theory A (IF 1.263) Pub Date : 20220106
Lei YuLet Qnr be the graph with vertex set {−1,1}n in which two vertices are joined if their Hamming distance is at most r. The edgeisoperimetric problem for Qnr is that: For every (n,r,M) such that 1≤r≤n and 1≤M≤2n, determine the minimum edgeboundary size of a subset of vertices of Qnr with a given size M. In this paper, we apply two different approaches to prove bounds for this problem. The first approach

A generalization of hyperbolic Pascal triangles J. Comb. Theory A (IF 1.263) Pub Date : 20211228
Hacène Belbachir, Fella Rami, László SzalayRecently a new generalization of Pascal's triangle, the family of socalled hyperbolic Pascal triangles (in short HPT) was introduced. In this paper, we consider a variation of HPT by replacing the two legsequences of the triangle by arbitrary sequences {αn}n≥0 and {βn}n≥0. Originally the legs were the constant 1 sequence. We describe some quantitative properties via recurrences relations, explicit

An improved lower bound for multicolor Ramsey numbers and a problem of Erdős J. Comb. Theory A (IF 1.263) Pub Date : 20211223
Will SawinThe multicolor Ramsey number problem asks, for each pair of natural numbers ℓ and t, for the largest ℓcoloring of a complete graph with no monochromatic clique of size t. Recent works of ConlonFerber and Wigderson have improved the longstanding lower bound for this problem. We make a further improvement by replacing an explicit graph appearing in their constructions by a random graph. Graphs useful

Some nonexistence results for (v,m,k,pq)strong external difference families J. Comb. Theory A (IF 1.263) Pub Date : 20211223
Ka Hin Leung, Theo Fanuela PrabowoIn this paper, we derive some restrictions and nonexistence results for (v,m,k,pq)strong external difference families (SEDFs), where p and q are primes. We first show that there is no abelian (v,m,k,p2)SEDF with m>2. If p>q, we show that if q+1 is a power of two; or q+1=2r or 4r for some prime r>3, then there is no abelian (v,m,k,pq)SEDF with m>2 for all sufficiently large primes p. Furthermore

Reconstructing Young tableaux J. Comb. Theory A (IF 1.263) Pub Date : 20211213
Alan J. Cain, Erkko LehtonenThis paper completely characterizes the standard Young tableaux that can be reconstructed from their sets or multisets of 1minors. In particular, any standard Young tableau with at least 5 entries can be reconstructed from its set of 1minors.

Divisor graphs and isotopy invariants of commutative quasigroups J. Comb. Theory A (IF 1.263) Pub Date : 20211213
John D. LaGrangeGiven an element x of a commutative quasigroup A, the xdivisor graph of A is the graph Γx(A) whose vertices are the elements of A such that distinct vertices a and b are adjacent if and only if ab=x. This paper examines how isotopies act on the set {Γx(A)  x∈A}. It is shown that if A<∞ is not a multiple of 4, then this set is an isotopy invariant. Moreover, under certain conditions (for example

Spectral fundamentals and characterizations of signed directed graphs J. Comb. Theory A (IF 1.263) Pub Date : 20211207
Pepijn Wissing, Edwin R. van DamThe spectral properties of signed directed graphs, which may be naturally obtained by assigning a sign to each edge of a directed graph, have received substantially less attention than those of their undirected and/or unsigned counterparts. To represent such signed directed graphs, we use a striking equivalence to T6gain graphs to formulate a Hermitian adjacency matrix, whose entries are the unit

Modular relations of the Tutte symmetric function J. Comb. Theory A (IF 1.263) Pub Date : 20211208
Logan Crew, Sophie SpirklFor a graph G, its Tutte symmetric function XBG generalizes both the Tutte polynomial TG and the chromatic symmetric function XG. We may also consider XB as a map from the textended Hopf algebra G[t] of labeled graphs to symmetric functions. We show that the kernel of XB is generated by vertexrelabellings and a finite set of modular relations, in the same style as a recent analogous result by Penaguião

MacMahon Partition Analysis: A discrete approach to broken stick problems J. Comb. Theory A (IF 1.263) Pub Date : 20211130
William VerreaultWe propose a discrete approach to solve problems on forming polygons from broken sticks, which is akin to counting polygons with sides of integer length subject to certain Diophantine inequalities. Namely, we use MacMahon's Partition Analysis to obtain a generating function for the size of the set of segments of a broken stick subject to these inequalities. In particular, we use this approach to show

Symmetric binary Steinhaus triangles and parityregular Steinhaus graphs J. Comb. Theory A (IF 1.263) Pub Date : 20211129
Jonathan ChappelonA binary Steinhaus triangle is a triangle of zeroes and ones that points down and with the same local rule as the Pascal triangle modulo 2. A binary Steinhaus triangle is said to be rotationally symmetric, horizontally symmetric or dihedrally symmetric if it is invariant under the 120 degrees rotation, the horizontal reflection or both, respectively. The first part of this paper is devoted to the study

On zerosum subsequences of length kexp(G) II J. Comb. Theory A (IF 1.263) Pub Date : 20211122
Weidong Gao, Siao Hong, Jiangtao PengLet G be an additive finite abelian group of exponent exp(G). For every positive integer k, let skexp(G)(G) denote the smallest integer t such that every sequence over G of length t has a zerosum subsequence of length kexp(G). Let ηkexp(G)(G) denote the smallest integer t such that every sequence over G of length t has a zerosum subsequence of length between 1 and kexp(G). It is conjectured

Infinite Sperner's theorem J. Comb. Theory A (IF 1.263) Pub Date : 20211117
Benny Sudakov, István Tomon, Adam Zsolt WagnerOne of the most classical results in extremal set theory is Sperner's theorem, which says that the largest antichain in the Boolean lattice 2[n] has size Θ(2nn). Motivated by an old problem of Erdős on the growth of infinite Sidon sequences, in this note we study the growth rate of maximum infinite antichains. Using the well known Kraft's inequality for prefix codes, it is not difficult to show that