Journal of Combinatorial Theory Series A最新文献

英文中文

The Weisfeiler-Leman stabilization of a tree 树的Weisfeiler-Leman稳定化

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-02-01 Epub Date: 2025-08-13 DOI: 10.1016/j.jcta.2025.106099

Jing Xu , Tatsuro Ito , Shuang-Dong Li

For the Weisfeiler-Leman stabilization, we introduce a concept, which we call the coherent length, to measure how long it takes. We show that the coherent length is at most 8 for trees, using the structures of their T-algebras and of the centralizer algebras of their automorphism groups.

对于Weisfeiler-Leman稳定化，我们引入了一个概念，我们称之为相干长度，来测量它需要多长时间。利用树的t代数及其自同构群的中心化代数的结构，证明了树的相干长度最多为8。

引用次数: 0

The existence of m-Haar graphical representations m-Haar图形表示的存在性

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-02-01 Epub Date: 2025-08-05 DOI: 10.1016/j.jcta.2025.106096

Jia-Li Du , Yan-Quan Feng , Binzhou Xia , Da-Wei Yang

Extending the well-studied concept of graphical regular representations to bipartite graphs, a Haar graphical representation (HGR) of a group G is a bipartite graph whose automorphism group is isomorphic to G and acts semiregularly with the orbits giving the bipartition. The question of which groups admit an HGR was inspired by a closely related question of Estélyi and Pisanski in 2016, as well as Babai's work in 1980 on poset representations, and has been recently solved by Morris and Spiga. In this paper, we introduce the m-Haar graphical representation (m-HGR) as a natural generalization of HGR to m-partite graphs for

m \geq 2

, and explore the existence of m-HGRs for any fixed group. This inquiry represents a more robust version of the existence problem of GmSRs as addressed by Du, Feng and Spiga in 2020. Our main result is a complete classification of finite groups G without m-HGRs.

将已被广泛研究的图形正则表示的概念推广到二部图，群G的Haar图形表示（HGR）是自同构群与G同构并与给出二分的轨道半正则作用的二部图。哪些群体承认HGR的问题受到了est和Pisanski在2016年提出的一个密切相关的问题的启发，以及Babai在1980年对posset表示的研究，莫里斯和斯皮加最近解决了这个问题。本文引入m- haar图表示（m-HGR）作为m≥2时m- haar图表示对m-部图的自然推广，并探讨了m-HGR对任意固定群的存在性。这项研究代表了杜、冯和斯皮加在2020年提出的gmsr存在问题的一个更强大的版本。我们的主要结果是没有m- hgr的有限群G的完全分类。

引用次数: 0

Step-constrained self-avoiding walks on finite grids 有限网格上的步长约束自回避行走

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-02-01 Epub Date: 2025-08-29 DOI: 10.1016/j.jcta.2025.106104

Hacène Belbachir , László Major , László Németh , László Szalay

The study of self-avoiding walks (SAWs) on integer lattices has been an area of active research for several decades. In this paper, we investigate the number of SAWs between two diagonally opposite corners in a finite rectangular subgraph of the integer lattice, subject to certain constraints. In the two–dimensional case, we provide an explicit formula for the number of SAWs of a prescribed length, restricted to three-step directions. In addition, we develop an algorithm that produces faster computational results than the explicit formula. For some special cases, we present detailed counts of the SAWs in question. For rectangular grid graphs of higher dimensions, we provide a formula to count the number of SAWs that are exactly two steps longer than the shortest walks.

整数格上的自回避行走（saw）是一个活跃的研究领域。在一定的约束条件下，我们研究了整数格的有限矩形子图中对角对角之间的saw的数目。在二维情况下，我们提供了一个明确的公式，规定长度的锯数，限制在三步方向。此外，我们开发了一种算法，比显式公式产生更快的计算结果。对于某些特殊情况，我们提供了有关saw的详细计数。对于高维的矩形网格图，我们提供了一个公式来计算恰好比最短步数长两步的saw的数量。

引用次数: 0

Existences of semiregular automorphisms of edge-transitive graphs of odd prime valency 奇素价边传递图的半正则自同构的存在性

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-02-01 Epub Date: 2025-09-18 DOI: 10.1016/j.jcta.2025.106117

Wenjuan Luo, Jing Xu

The Polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism whose cycles all have the same length. Similarly, in [11] the authors asked if every connected regular edge-transitive graph admits a semiregular automorphism. In this paper we prove that edge-transitive graphs of odd prime valency have a semiregular automorphism.

多循环猜想断言每个顶点传递有向图都有一个环长度相同的半正则自同构。类似地，在[11]中，作者问是否每个连通正则边传递图都承认一个半正则自同构。证明了奇素价边传递图具有半正则自同构。

引用次数: 0

On the number of subsequence sums related to the support of a sequence in finite abelian groups 有限阿贝尔群中与序列支持度相关的子序列和的数目

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-02-01 Epub Date: 2025-10-24 DOI: 10.1016/j.jcta.2025.106124

Rui Wang, Han Chao, Jiangtao Peng

Let G be a finite abelian group and S a sequence with elements of G. Let

| S |

denote the length of S and

supp (S)

the set of all the distinct terms in S. For an integer k with

k \in [1, | S |]

, let

Σ_{k} (S) \subset G

denote the set of group elements which can be expressed as a sum of a subsequence of S with length k. Let

Σ (S) = \cup_{k = 1}^{| S |} Σ_{k} (S)

and

Σ_{\geq k} (S) = \cup_{t = k}^{| S |} Σ_{t} (S)

. It is known that if

0 \notin Σ (S)

, then

| Σ (S) | \geq | S | + | supp (S) | - 1

. In this paper, we determine the structure of a sequence S satisfying

0 \notin Σ (S)

and

| Σ (S) | = | S | + | supp (S) | - 1

. As a consequence, we can give a counterexample of a conjecture of Gao, Grynkiewicz, and Xia. Moreover, we prove that if

| S | > k

and

0 \notin Σ_{\geq k} (S) \cup supp (S)

, then

| Σ_{\geq k} (S) | \geq | S | - k + | supp (S) |

. Then we can give an alternative proof of a conjecture of Hamidoune, which was first proved by Gao, Grynkiewicz, and Xia.

设G是一个有限阿贝尔群，S是一个具有G元素的序列，设|S|表示S的长度，supp(S)表示S中所有不同项的集合。对于k∈[1，|S|]的整数k，设Σk(S)∧G表示可以表示为长度为k的S的子序列的和的群元素集合，设Σ(S)=∪k=1|S|Σk(S)和Σ≥k(S)=∪t=k|S|Σt(S)。众所周知,如果0∉Σ(S),然后|Σ(S) |≥| | + |增刊(S) |−1。本文确定了满足0∈Σ(S)和|Σ(S)|=|S|+|supp(S)|−1的序列S的结构。因此，我们可以给出Gao、Grynkiewicz和Xia猜想的一个反例。此外,我们证明如果| |在k和0∉Σ≥k (S)∪增刊(S),然后|Σ≥k (S) |≥|年代|−k + |增刊(S) |。然后，我们可以给出由Gao、Grynkiewicz和Xia首先证明的Hamidoune猜想的另一种证明。

引用次数: 0

Semicomplete multipartite weakly distance-regular digraphs 半完全多部弱距离正则有向图

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-02-01 Epub Date: 2025-10-28 DOI: 10.1016/j.jcta.2025.106125

Shuang Li , Yuefeng Yang , Kaishun Wang

A digraph is semicomplete multipartite if its underlying graph is a complete multipartite graph. As a special case of semicomplete multipartite digraphs, Jørgensen et al. [7] initiated the study of doubly regular team tournaments. As a natural extension, we introduce doubly regular team semicomplete multipartite digraphs and show that such digraphs fall into three types. Furthermore, we give a characterization of all semicomplete multipartite commutative weakly distance-regular digraphs.

如果一个有向图的底图是一个完全多部图，那么它就是半完全多部图。作为半完全多部有向图的特例，Jørgensen et al. b[7]发起了双常规团队比赛的研究。作为一种自然推广，我们引入了双正则团队半完全多部有向图，并证明了这类有向图可分为三种类型。进一步，我们给出了所有半完全多部可交换弱距离正则有向图的一个刻画。

引用次数: 0

Combinatorial interpretation of the Schlesinger–Zudilin stuffle product Schlesinger-Zudilin填充物积的组合解释

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-02-01 Epub Date: 2025-08-28 DOI: 10.1016/j.jcta.2025.106103

Benjamin Brindle

We derive an explicit formula for the quasi–shuffle product satisfied by Schlesinger–Zudilin Multiple q-Zeta Values, expressed in terms of partition data. To achieve this, we interpret Schlesinger–Zudilin Multiple q-Zeta Values as generating series of distinguished marked partitions, which are partitions whose Young diagrams have certain rows and columns marked. Together with the description of duality using marked partitions in [4], and Bachmann's conjecture ([1]) that all linear relations among Multiple q-Zeta Values are implied by duality and the stuffle product, this paper completes the description of the conjectural structure of Multiple q-Zeta Values using marked partitions.

给出了用分区数据表示的Schlesinger-Zudilin多重q-Zeta值所满足的拟洗牌积的显式公式。为了实现这一点，我们将Schlesinger-Zudilin Multiple q-Zeta值解释为生成一系列区分标记的分区，这些分区的Young图中标记了某些行和列。结合[4]中使用标记分区对对偶性的描述，以及Bachmann关于多个q-Zeta值之间的所有线性关系都由对偶性和填充积隐含的猜想（[1]），本文完成了对多个q-Zeta值使用标记分区的推测结构的描述。

引用次数: 0

Induced arithmetic removal for partition-regular patterns of complexity 1 复杂度为1的分区规则模式的诱导算法去除

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-02-01 Epub Date: 2025-11-04 DOI: 10.1016/j.jcta.2025.106126

V. Gladkova

In 2019, Fox, Tidor and Zhao [7] proved an induced arithmetic removal lemma for linear patterns of complexity 1 in vector spaces over a fixed finite field. With no further assumptions on the pattern, this induced removal lemma cannot guarantee a fully pattern-free recolouring of the space, as some ‘non-generic’ instances must necessarily remain. On the other hand, Bhattacharyya, Fischer, H. Hatami, P. Hatami, and Lovett [3] showed in 2012 that in the case of translation-invariant patterns, it is possible to obtain recolourings that eliminate the given pattern completely, with no exceptions left behind. This paper demonstrates that such complete removal can be achieved for all partition-regular patterns of complexity 1.

在2019年，Fox， Tidor和Zhao[7]证明了在固定有限域上向量空间中复杂度为1的线性模式的诱导算法去除引理。由于没有对图案的进一步假设，这种诱导去除引理不能保证空间完全无图案的重新着色，因为一些“非一般”实例必须保留。另一方面，Bhattacharyya, Fischer， H. Hatami， P. Hatami和Lovett[3]在2012年表明，对于平移不变模式，可以获得完全消除给定模式的再着色，没有任何例外。本文证明了对于复杂度为1的所有分区规则模式都可以实现这种完全去除。

引用次数: 0

On nontrivial cross-t-intersecting families 关于非平凡的交叉交集族

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01 Epub Date: 2025-08-01 DOI: 10.1016/j.jcta.2025.106095

Dongang He , Anshui Li , Biao Wu , Huajun Zhang

Two families

A \subseteq (\begin{matrix} [n] \\ k \end{matrix})

and

B \subseteq (\begin{matrix} [n] \\ ℓ \end{matrix})

are called nontrivial cross-t-intersecting if

| A \cap B | \geq t

for all

A \in A

B \in B

and

| ⋂_{A \in A \cup B} A | < t

. In this paper we will determine the upper bound of

| A | | B |

for nontrivial cross-t-intersecting families

A \subseteq (\begin{matrix} [n] \\ k \end{matrix})

and

B \subseteq (\begin{matrix} [n] \\ ℓ \end{matrix})

for positive integers n, k, ℓ and t such that

n \geq \max {(t + 1) (k - t + 1), (t + 1) (ℓ - t + 1)}

and

t \geq 3

. The structures of the extremal families attaining the upper bound are also characterized. As a byproduct of the main result in this paper, one product version of Erdős–Ko–Rado Theorem for two families of cross-t-intersecting can be easily obtained which gives a confirmative answer to one conjecture by Tokushige.

对于所有A∈A， B∈B, |A∈A∪BA|<t，当|A∩B|≥t时，称两个族A （[n]k）和B （[n] r）为非平凡正交相交。在正整数n、k、r、t的条件下，确定非平凡正交族A （[n]k）和B （[n] r）的|A||B|的上界，使n≥max (t+1)(k−t+1),(t+1)(r−t+1)}, t≥3。对达到上界的极族结构也进行了表征。作为本文主要结果的副产品，我们可以很容易地得到两族交叉相交的Erdős-Ko-Rado定理的一个乘积版本，从而证实了Tokushige的一个猜想。

引用次数: 0

Combinatorics on bi-γ-positivity of 1/k-Eulerian polynomials 1/k-欧拉多项式双γ正性的组合

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01 Epub Date: 2025-07-02 DOI: 10.1016/j.jcta.2025.106092

Sherry H.F. Yan , Xubo Yang , Zhicong Lin

The

1 / k

-Eulerian polynomials

A_{n}^{(k)} (x)

were introduced as ascent polynomials over k-inversion sequences by Savage and Viswanathan. The bi-γ-positivity of the

1 / k

-Eulerian polynomials

A_{n}^{(k)} (x)

was known but to give a combinatorial interpretation of the corresponding bi-γ-coefficients still remains open. The study of the theme of bi-γ-positivity from a purely combinatorial aspect was proposed by Athanasiadis. In this paper, we provide a combinatorial interpretation for the bi-γ-coefficients of

A_{n}^{(k)} (x)

by using the model of certain ordered labeled forests. Our combinatorial approach consists of three main steps:

•
construct a bijection between k-Stirling permutations and certain forests that are named increasing pruned even k-ary forests;
•
introduce a generalized Foata–Strehl action on increasing pruned even k-ary trees which implies the longest ascent-plateau polynomials over k-Stirling permutations with initial letter 1 are γ-positive, a result that may have independent interest;
•
develop two crucial transformations on increasing pruned even k-ary forests to conclude our combinatorial interpretation.

1/k欧拉多项式An(k)(x)由Savage和Viswanathan作为k-反转序列上的上升多项式引入。1/k-欧拉多项式An(k)(x)的双γ正性是已知的，但给出相应的双γ系数的组合解释仍然是开放的。从纯组合的角度研究双γ正性的主题是由Athanasiadis提出的。本文利用有序标记森林模型，给出了An(k)(x)的双γ-系数的组合解释。我们的组合方法包括三个主要步骤：•在k-Stirling排列和某些被命名为增加修剪偶数k-ary森林的森林之间构造一个双射；•在增加修剪偶数k-ary树上引入一个广义的fota - strehl作用，该作用表明k-Stirling排列上的首字母为1的最长上升-高原多项式是γ-正的。•发展两个关键的转变，增加修剪甚至k-ary森林，以结束我们的组合解释。

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