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Distribution of maxima and minima statistics on alternating permutations, Springer numbers, and avoidance of flat POPs J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-28
Tian Han, Sergey Kitaev, Philip B. ZhangIn this paper, we find distributions of the left-to-right maxima, right-to-left maxima, left-to-right minima and right-to-left-minima statistics on up-down and down-up permutations of even and odd lengths. We recover and generalize a result by Carlitz and Scoville, obtained in 1975, stating that the distribution of left-to-right maxima on down-up permutations of even length is given by (sec(t))q.
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Flag transitive geometries with trialities and no dualities coming from Suzuki groups J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-27
Dimitri Leemans, Klara Stokes, Philippe TranchidaRecently, Leemans and Stokes constructed an infinite family of incidence geometries admitting trialities but no dualities from the groups PSL(2,q) (where q=p3n with p a prime and n>0 a positive integer). Unfortunately, these geometries are not flag transitive. In this paper, we work with the Suzuki groups Sz(q), where q=22e+1 with e a positive integer and 2e+1 is divisible by 3. For any odd integer
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Multivariate P- and/or Q-polynomial association schemes J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-27
Eiichi Bannai, Hirotake Kurihara, Da Zhao, Yan ZhuThe classification problem of P- and Q-polynomial association schemes has been one of the central problems in algebraic combinatorics. Generalizing the concept of P- and Q-polynomial association schemes to multivariate cases, namely to consider higher rank P- and Q-polynomial association schemes, has been tried by some authors, but it seems that so far there were neither very well-established definitions
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More on r-cross t-intersecting families for vector spaces J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-26
Tian Yao, Dehai Liu, Kaishun WangLet V be a finite dimensional vector space over a finite field. Suppose that F1, F2, …, Fr are r-cross t-intersecting families of k-subspaces of V. In this paper, we determine the extremal structure when ∏i=1r|Fi| is maximum under the condition that dim(⋂F∈FiF)
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Regular ovoids and Cameron-Liebler sets of generators in polar spaces J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-25
Maarten De Boeck, Jozefien D'haeseleer, Morgan RodgersCameron-Liebler sets of generators in polar spaces were introduced a few years ago as natural generalisations of the Cameron-Liebler sets of subspaces in projective spaces. In this article we present the first two constructions of non-trivial Cameron-Liebler sets of generators in polar spaces. Also regular m-ovoids of k-spaces are introduced as a generalization of m-ovoids of polar spaces. They are
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On common energies and sumsets J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-24
Shkredov I.D.We obtain a polynomial criterion for a set to have a small doubling in terms of the common energy of its subsets.
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Structure of Terwilliger algebras of quasi-thin association schemes J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-24
Zhenxian Chen, Changchang XiWe show that the Terwilliger algebra of a quasi-thin association scheme over a field is always a quasi-hereditary cellular algebra in the sense of Cline-Parshall-Scott and of Graham-Lehrer, respectively, and that the basic algebra of the Terwilliger algebra is the dual extension of a star with all arrows pointing to its center if the field has characteristic 2. Thus many homological and representation-theoretic
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Simple geometric mitosis J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-24
Valentina KiritchenkoWe construct simple geometric operations on faces of the Cayley sum of two polytopes. These operations can be thought of as convex geometric counterparts of divided difference operators in Schubert calculus. We show that these operations give a uniform construction of Knutson–Miller mitosis in the type A and Fujita mitosis in the type C on Kogan faces of Gelfand–Zetlin polytopes.
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Truncated forms of MacMahon's q-series J. Comb. Theory A (IF 0.9) Pub Date : 2025-02-24
Mircea MercaIn 1920, Percy Alexander MacMahon defined the partition generating functionsAk(q):=∑0
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A symmetry on weakly increasing trees and multiset Schett polynomials J. Comb. Theory A (IF 0.9) Pub Date : 2025-01-20
Zhicong Lin, Jun MaBy considering the parity of the degrees and levels of nodes in increasing trees, a new combinatorial interpretation for the coefficients of the Taylor expansions of the Jacobi elliptic functions is found. As one application of this new interpretation, a conjecture of Ma–Mansour–Wang–Yeh is solved. Unifying the concepts of increasing trees and plane trees, Lin–Ma–Ma–Zhou introduced weakly increasing
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On recursive constructions for 2-designs over finite fields J. Comb. Theory A (IF 0.9) Pub Date : 2025-01-20
Xiaoran Wang, Junling ZhouThis paper concentrates on recursive constructions for 2-designs over finite fields. In 1998, Itoh presented a powerful recursive construction: for certain index λ, if there exists a Singer cycle invariant 2-(l,3,λ)q design, then there also exists an SL(m,ql) invariant 2-(ml,3,λ)q design for all integers m≥3. We investigate the GL(m,ql)-incidence matrix between 2-subspaces and k-subspaces of GF(q)ml
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There are no good infinite families of toric codes J. Comb. Theory A (IF 0.9) Pub Date : 2025-01-17
Jason P. Bell, Sean Monahan, Matthew Satriano, Karen Situ, Zheng XieSoprunov and Soprunova posed a question on the existence of infinite families of toric codes that are “good” in a precise sense. We prove that such good families do not exist by proving a more general Szemerédi-type result: for all c∈(0,1] and all positive integers N, subsets of density at least c in {0,1,…,N−1}n contain hypercubes of arbitrarily large dimension as n grows.
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Unique representations of integers by linear forms J. Comb. Theory A (IF 0.9) Pub Date : 2025-01-17
Sándor Z. Kiss, Csaba SándorLet k≥2 be an integer and let A be a set of nonnegative integers. For a k-tuple of positive integers λ_=(λ1,…,λk) with 1≤λ1<λ2<⋯<λk, we define the additive representation function RA,λ_(n)=|{(a1,…,ak)∈Ak:λ1a1+⋯+λkak=n}|. For k=2, Moser constructed a set A of nonnegative integers such that RA,λ_(n)=1 holds for every nonnegative integer n. In this paper we characterize all the k-tuples λ_ and the sets
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On a conjecture concerning the r-Euler-Mahonian statistic on permutations J. Comb. Theory A (IF 0.9) Pub Date : 2025-01-17
Kaimei Huang, Zhicong Lin, Sherry H.F. YanA pair (st1,st2) of permutation statistics is said to be r-Euler-Mahonian if (st1,st2) and (rdes, rmaj) are equidistributed over the set Sn of all permutations of {1,2,…,n}, where rdes denotes the r-descent number and rmaj denotes the r-major index introduced by Rawlings. The main objective of this paper is to prove that (excr,denr) and (rdes, rmaj) are equidistributed over Sn, thereby confirming a
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Full weight spectrum one-orbit cyclic subspace codes J. Comb. Theory A (IF 0.9) Pub Date : 2024-12-31
Chiara Castello, Olga Polverino, Ferdinando ZulloFor a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper, we will focus on the analogous class of codes within the framework of cyclic subspace codes. Cyclic subspace codes have garnered significant attention, particularly for
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Contributions to Ma's conjecture concerning abelian difference sets with multiplier −1 (I) J. Comb. Theory A (IF 0.9) Pub Date : 2024-12-31
Yasutsugu Fujita, Maohua LeLet N, P be the sets of all positive integers and odd primes, respectively. In 1991, when studying the existence of abelian difference sets with multiplier −1, S.-L. Ma [14] conjectured that the equation (⁎)x2=22a+2p2n−2a+2pm+n+1, p∈P,x,z,m,n∈N has only one solution (p,x,a,m,n)=(5,49,3,2,1). This is a far from solved problem that has been poorly known for so long. In this paper, using some elementary
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Diametric problem for permutations with the Ulam metric (optimal anticodes) J. Comb. Theory A (IF 0.9) Pub Date : 2024-12-19
Pat Devlin, Leo DouhovnikoffWe study the diametric problem (i.e., optimal anticodes) in the space of permutations under the Ulam distance. That is, let Sn denote the set of permutations on n symbols, and for each σ,τ∈Sn, define their Ulam distance as the number of distinct symbols that must be deleted from each until they are equal. We obtain a near-optimal upper bound on the size of the intersection of two balls in this space
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Sidon sets, thin sets, and the nonlinearity of vectorial Boolean functions J. Comb. Theory A (IF 0.9) Pub Date : 2024-12-19
Gábor P. NagyThe vectorial nonlinearity of a vector-valued function is its distance from the set of affine functions. In 2017, Liu, Mesnager, and Chen conjectured a general upper bound for the vectorial linearity. Recently, Carlet established a lower bound in terms of differential uniformity. In this paper, we improve Carlet's lower bound. Our approach is based on the fact that the level sets of a vectorial Boolean
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On the size of integer programs with bounded non-vanishing subdeterminants J. Comb. Theory A (IF 0.9) Pub Date : 2024-12-18
Björn Kriepke, Gohar M. Kyureghyan, Matthias SchymuraMotivated by complexity questions in integer programming, this paper aims to contribute to the understanding of combinatorial properties of integer matrices of row rank r and with bounded subdeterminants. In particular, we study the column number question for integer matrices whose every r×r minor is non-zero and bounded by a fixed constant Δ in absolute value. Approaching the problem in two different
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Cayley extensions of maniplexes and polytopes J. Comb. Theory A (IF 0.9) Pub Date : 2024-12-18
Gabe Cunningham, Elías Mochán, Antonio MonteroA map on a surface whose automorphism group has a subgroup acting regularly on its vertices is called a Cayley map. Here we generalize that notion to maniplexes and polytopes. We define M to be a Cayley extension of K if the facets of M are isomorphic to K and if some subgroup of the automorphism group of M acts regularly on the facets of M. We show that many natural extensions in the literature on
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On joint short minimal zero-sum subsequences over finite abelian groups of rank two J. Comb. Theory A (IF 0.9) Pub Date : 2024-12-03
Yushuang Fan, Qinghai ZhongLet (G,+,0) be a finite abelian group and let ηN(G) be the smallest integer ℓ such that every sequence over G∖{0} of length ℓ has two joint short minimal zero-sum subsequences. In 2013, Gao et al. obtained that ηN(Cn⊕Cn)=3n+1 for every n≥2 and solved the corresponding inverse problem for groups Cp⊕Cp, where p is a prime. In this paper, we determine the precise value of ηN(G) for all finite abelian
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The degree of functions in the Johnson and q-Johnson schemes J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-29
Michael Kiermaier, Jonathan Mannaert, Alfred WassermannIn 1982, Cameron and Liebler investigated certain special sets of lines in PG(3,q), and gave several equivalent characterizations. Due to their interesting geometric and algebraic properties, these Cameron-Liebler line classes got much attention. Several generalizations and variants have been considered in the literature, the main directions being a variation of the dimensions of the involved spaces
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Sequence reconstruction problem for deletion channels: A complete asymptotic solution J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-27
Van Long Phuoc Pham, Keshav Goyal, Han Mao KiahTransmit a codeword ▪, that belongs to an (ℓ−1)-deletion-correcting code of length n, over a t-deletion channel for some 1≤ℓ≤t
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A classification of the flag-transitive 2-(v,k,2) designs J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-26
Hongxue Liang, Alessandro MontinaroIn this paper, we provide a complete classification of 2-(v,k,2) designs admitting a flag-transitive automorphism group of affine type with the only exception of the semilinear 1-dimensional group. Alongside this analysis, we provide a construction of seven new families of such flag-transitive 2-designs, one of them infinite, and some of them involving remarkable objects such as t-spreads, translation
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Distributions of reciprocal sums of parts in integer partitions J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-26
Byungchan Kim, Eunmi KimLet Dn be the set of partitions of n into distinct parts, and srp(λ) be the sum of reciprocals of the parts of the partition λ. We show that as n→∞,E[srp(λ):λ∈Dn]∼log(3n)4andVar[srp(λ):λ∈Dn]∼π224. Moreover, for Pn, the set of ordinary partitions of n, we show that as n→∞,E[srp(λ):λ∈Pn]∼πn6andVar[srp(λ):λ∈Pn]∼π215n. To prove these asymptotic formulas in a uniform manner, we derive a general asymptotic
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Non-empty pairwise cross-intersecting families J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-26
Yang Huang, Yuejian PengTwo families A and B are cross-intersecting if A∩B≠∅ for any A∈A and B∈B. We call t families A1,A2,…,At pairwise cross-intersecting families if Ai and Aj are cross-intersecting for 1≤i
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Dominance complexes, neighborhood complexes and combinatorial Alexander duals J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-16
Takahiro Matsushita, Shun WakatsukiWe show that the dominance complex D(G) of a graph G coincides with the combinatorial Alexander dual of the neighborhood complex N(G‾) of the complement of G. Using this, we obtain a relation between the chromatic number χ(G) of G and the homology group of D(G). We also obtain several known results related to dominance complexes from well-known facts of neighborhood complexes. After that, we suggest
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The vector space generated by permutations of a trade or a design J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-06
E. Ghorbani, S. Kamali, G.B. KhosrovshahiMotivated by a classical result of Graver and Jurkat (1973) and Graham, Li, and Li (1980) in combinatorial design theory, which states that the permutations of t-(v,k) minimal trades generate the vector space of all t-(v,k) trades, we investigate the vector space spanned by permutations of an arbitrary trade. We prove that this vector space possesses a decomposition as a direct sum of subspaces formed
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Upper bounds for the number of substructures in finite geometries from the container method J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-06
Sam Mattheus, Geertrui Van de VoordeWe use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial ovoids and EKR-sets of flags in polar spaces, line spreads in PG(2r−1,q) and plane spreads in PG(5,q), and caps in PG(3,q). The latter result extends work due to
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Some conjectures of Ballantine and Merca on truncated sums and the minimal excludant in congruences classes J. Comb. Theory A (IF 0.9) Pub Date : 2024-11-05
Olivia X.M. YaoIn 2012, Andrews and Merca proved a truncated theorem on Euler's pentagonal number theorem. Since then, a number of results on truncated theta series have been proved. In this paper, we find the connections between truncated sums of certain partition functions and the minimal excludant statistic which has been found to exhibit connections with a handful of objects such as Dyson's crank. We present
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Reconstruction of hypermatrices from subhypermatrices J. Comb. Theory A (IF 0.9) Pub Date : 2024-10-22
Wenjie Zhong, Xiande ZhangFor a given n, what is the smallest number k such that every sequence of length n is determined by the multiset of all its k-subsequences? This is called the k-deck problem for sequence reconstruction, and has been generalized to the two-dimensional case – reconstruction of n×n-matrices from submatrices. Previous works show that the smallest k is at most O(n12) for sequences and at most O(n23) for
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Direct constructions of column-orthogonal strong orthogonal arrays J. Comb. Theory A (IF 0.9) Pub Date : 2024-10-18
Jingjun Bao, Lijun Ji, Juanjuan XuStrong orthogonal arrays have better space-filling properties than ordinary orthogonal arrays for computer experiments. Strong orthogonal arrays of strengths two plus, two star and three minus can improve the space-filling properties in low dimensions and column orthogonality plays a vital role in computer experiments. In this paper, we use difference matrices and generator matrices of linear codes
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Indecomposable combinatorial games J. Comb. Theory A (IF 0.9) Pub Date : 2024-10-15
Michael Fisher, Neil A. McKay, Rebecca Milley, Richard J. Nowakowski, Carlos P. SantosIn Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If there are no such summands, then the form is indecomposable. The main contribution of this document is the characterization of the indecomposable nimbers and the
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Neighborly partitions, hypergraphs and Gordon's identities J. Comb. Theory A (IF 0.9) Pub Date : 2024-10-04
Pooneh Afsharijoo, Hussein MourtadaWe prove a family of partition identities which is “dual” to the family of Andrews-Gordon's identities. These identities are inspired by a correspondence between a special type of partitions and “hypergraphs” and their proof uses combinatorial commutative algebra.
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Point-line geometries related to binary equidistant codes J. Comb. Theory A (IF 0.9) Pub Date : 2024-10-04
Mark Pankov, Krzysztof Petelczyc, Mariusz ŻynelPoint-line geometries whose singular subspaces correspond to binary equidistant codes are investigated. The main result is a description of automorphisms of these geometries. In some important cases, automorphisms induced by non-monomial linear automorphisms surprisingly arise.
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On locally n × n grid graphs J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-26
Carmen Amarra, Wei Jin, Cheryl E. PraegerWe investigate locally n×n grid graphs, that is, graphs in which the neighbourhood of any vertex is the Cartesian product of two complete graphs on n vertices. We consider the subclass of these graphs for which each pair of vertices at distance two is joined by sufficiently many paths of length 2. The number of such paths is known to be at most 2n by previous work of Blokhuis and Brouwer. We show that
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On power monoids and their automorphisms J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-25
Salvatore Tringali, Weihao YanEndowed with the binary operation of set addition, the family Pfin,0(N) of all finite subsets of N containing 0 forms a monoid, with the singleton {0} as its neutral element.
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On non-empty cross-t-intersecting families J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-24
Anshui Li, Huajun ZhangLet A1,A2,…,Am be families of k-element subsets of a n-element set. We call them cross-t-intersecting if |Ai∩Aj|≥t for any Ai∈Ai and Aj∈Aj with i≠j. In this paper we will prove that, for n≥2k−t+1, if A1,A2,…,Am are non-empty cross-t-intersecting families, then∑1≤i≤m|Ai|≤max{(nk)−∑1≤i≤t−1(ki)(n−kk−i)+m−1,mM(n,k,t)}, where M(n,k,t) is the size of the maximum t-intersecting family of ([n]k). Moreover
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Avoiding intersections of given size in finite affine spaces AG(n,2) J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-24
Benedek Kovács, Zoltán Lóránt NagyWe study the set of intersection sizes of a k-dimensional affine subspace and a point set of size m∈[0,2n] of the n-dimensional binary affine space AG(n,2). Following the theme of Erdős, Füredi, Rothschild and T. Sós, we partially determine which local densities in k-dimensional affine subspaces are unavoidable in all m-element point sets in the n-dimensional affine space.
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A rank two Leonard pair in Terwilliger algebras of Doob graphs J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-23
John Vincent S. MoralesLet Γ=Γ(n,m) denote the Doob graph formed by the Cartesian product of the nth Cartesian power of the Shrikhande graph and the mth Cartesian power of the complete graph on four vertices. Let T=T(x) denote the Terwilliger algebra of Γ with respect to a fixed vertex x of Γ and let W denote an arbitrary non-thin irreducible T-module in the standard module of Γ. In (Morales and Palma, 2021 [25]), it was
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Covering the set of p-elements in finite groups by proper subgroups J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-20
Attila Maróti, Juan Martínez, Alexander MoretóLet p be a prime and let G be a finite group which is generated by the set Gp of its p-elements. We show that if G is solvable and not a p-group, then the minimal number σp(G) of proper subgroups of G whose union contains Gp is equal to 1 less than the minimal number of proper subgroups of G whose union is G. For p-solvable groups G, we always have σp(G)≥p+1. We study the case of alternating and symmetric
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Proofs of some conjectures of Merca on truncated series involving the Rogers-Ramanujan functions J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-19
Yongqiang Chen, Olivia X.M. YaoIn 2012, Andrews and Merca investigated the truncated version of the Euler pentagonal number theorem. Their work has opened up a new study on truncated theta series and has inspired several mathematicians to work on the topic. In 2019, Merca studied the Rogers-Ramanujan functions and posed three groups of conjectures on truncated series involving the Rogers-Ramanujan functions. In this paper, we present
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On the proportion of metric matroids whose Jacobians have nontrivial p-torsion J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-16
Sergio Ricardo Zapata CeballosWe study the proportion of metric matroids whose Jacobians have nontrivial p-torsion. We establish a correspondence between these Jacobians and the Fp-rational points on configuration hypersurfaces, thereby relating their proportions. By counting points over finite fields, we prove that the proportion of these Jacobians is asymptotically equivalent to 1/p.
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Approximate generalized Steiner systems and near-optimal constant weight codes J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-11
Miao Liu, Chong ShangguanConstant weight codes (CWCs) and constant composition codes (CCCs) are two important classes of codes that have been studied extensively in both combinatorics and coding theory for nearly sixty years. In this paper we show that for all fixed odd distances, there exist near-optimal CWCs and CCCs asymptotically achieving the classic Johnson-type upper bounds.
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A note on tournament m-semiregular representations of finite groups J. Comb. Theory A (IF 0.9) Pub Date : 2024-09-04
Jia-Li DuFor a positive integer m, a group G is said to admit a tournament m-semiregular representation (TmSR for short) if there exists a tournament Γ such that the automorphism group of Γ is isomorphic to G and acts semiregularly on the vertex set of Γ with m orbits. It is easy to see that every finite group of even order does not admit a TmSR for any positive integer m. The T1SR is the well-known tournament
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The separating Noether number of abelian groups of rank two J. Comb. Theory A (IF 0.9) Pub Date : 2024-08-29
Barna ScheflerThe exact value of the separating Noether number of an arbitrary finite abelian group of rank two is determined. This is done by a detailed study of the monoid of zero-sum sequences over the group.
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Young tableau reconstruction via minors J. Comb. Theory A (IF 0.9) Pub Date : 2024-08-26
William Q. Erickson, Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski, Cordell Hammon, Jasmin Mohn, Indalecio Ruiz-BolanosThe tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau T, a 1-minor of T is a tableau obtained by first deleting any cell of T, and then performing jeu de taquin slides to fill the resulting gap. This can be iterated to arrive at the set of k-minors of T. The problem is this: given k, what are the values of n such that every tableau of
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Some expansion formulas for q-series and their applications J. Comb. Theory A (IF 0.9) Pub Date : 2024-08-12
Bing He, Suzhen WenIn this paper, we establish some general expansion formulas for q-series. Three of Liu's identities motivate us to search and find such type of formulas. These expansion formulas include as special cases or limiting cases many q-identities including the q-Gauss summation formula, the q-Pfaff-Saalschütz summation formula, three of Jackson's transformation formulas and Sears' terminating ϕ34 transformation
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r-Euler-Mahonian statistics on permutations J. Comb. Theory A (IF 0.9) Pub Date : 2024-08-06
Shao-Hua LiuLet and denote the permutation statistics -descent number and -excedance number, respectively. We prove that the pairs of permutation statistics and are equidistributed, where denotes the -major index defined by Don Rawlings and denotes the -Denert's statistic defined by Guo-Niu Han. When , this result reduces to the equidistribution of and , which was conjectured by Denert in 1990 and proved that
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The q-Onsager algebra and the quantum torus J. Comb. Theory A (IF 0.9) Pub Date : 2024-08-02
Owen GoffThe -Onsager algebra, denoted , is defined by two generators and two relations called the -Dolan-Grady relations. Recently, Terwilliger introduced some elements of , said to be alternating. These elements are denoted
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An infinite family of hyperovals of Q+(5,q), q even J. Comb. Theory A (IF 0.9) Pub Date : 2024-08-01
Bart De BruynWe construct an infinite family of hyperovals on the Klein quadric , even. The construction makes use of ovoids of the symplectic generalized quadrangle that is associated with an elliptic quadric which arises as solid intersection with . We also solve the isomorphism problem: we determine necessary and sufficient conditions for two hyperovals arising from the construction to be isomorphic.
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A proof of the Etzion-Silberstein conjecture for monotone and MDS-constructible Ferrers diagrams J. Comb. Theory A (IF 0.9) Pub Date : 2024-07-24
Alessandro Neri, Mima StanojkovskiFerrers diagram rank-metric codes were introduced by Etzion and Silberstein in 2009. In their work, they proposed a conjecture on the largest dimension of a space of matrices over a finite field whose nonzero elements are supported on a given Ferrers diagram and all have rank lower bounded by a fixed positive integer . Since stated, the Etzion-Silberstein conjecture has been verified in a number of
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New string attractor-based complexities for infinite words J. Comb. Theory A (IF 0.9) Pub Date : 2024-07-18
Julien Cassaigne, France Gheeraert, Antonio Restivo, Giuseppe Romana, Marinella Sciortino, Manon StipulantiA is a set of positions in a word such that each distinct factor has an occurrence crossing a position from the set. This definition comes from the data compression field, where the size of a smallest string attractor represents a lower bound for the output size of a large family of string compressors exploiting repetitions in words, including BWT-based and LZ-based compressors. For finite words, the
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Cluster braid groups of Coxeter-Dynkin diagrams J. Comb. Theory A (IF 0.9) Pub Date : 2024-07-10
Zhe Han, Ping He, Yu QiuCluster exchange groupoids are introduced by King-Qiu as an enhancement of cluster exchange graphs to study stability conditions and quadratic differentials. In this paper, we introduce the cluster exchange groupoid for any finite Coxeter-Dynkin diagram Δ and show that its fundamental group is isomorphic to the corresponding braid group associated with Δ.
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Restricted bargraphs and unimodal compositions J. Comb. Theory A (IF 0.9) Pub Date : 2024-07-05
Rigoberto Flórez, José L. Ramírez, Diego VillamizarIn this paper, we present a study on , which are polygons created by connecting unit squares along their edges. Specifically, we focus on a related concept called a , which is a path on a lattice in traced along the boundaries of a column convex polyomino where the lower edge is on the -axis. To explore new variations of bargraphs, we introduce the notion of , which incorporate an additional restriction
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Positivity and tails of pentagonal number series J. Comb. Theory A (IF 0.9) Pub Date : 2024-07-04
Nian Hong ZhouIn this paper, we refine a result of Andrews and Merca on truncated pentagonal number series. Subsequently, we establish some positivity results involving Andrews–Gordon–Bressoud identities and -regular partitions. In particular, we prove several conjectures of Merca and Krattenthaler–Merca–Radu on truncated pentagonal number series.
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On the difference of the enhanced power graph and the power graph of a finite group J. Comb. Theory A (IF 0.9) Pub Date : 2024-06-21
Sucharita Biswas, Peter J. Cameron, Angsuman Das, Hiranya Kishore DeyThe difference graph of a finite group is the difference of the enhanced power graph of and the power graph of , where all isolated vertices are removed. In this paper we study the connectedness and perfectness of with respect to various properties of the underlying group . We also find several connections between the difference graph of and the Gruenberg-Kegel graph of . We also examine the operation
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Flag-transitive automorphism groups of 2-designs with λ ≥ (r,λ)2 are not product type J. Comb. Theory A (IF 0.9) Pub Date : 2024-06-19
Huiling Li, Zhilin Zhang, Shenglin ZhouIn this note we show that a flag-transitive automorphism group of a non-trivial 2- design with is not of product action type. In conclusion, is a primitive group of affine or almost simple type.