European Journal of Combinatorics最新文献

英文中文

A weighted Murnaghan–Nakayama rule for (P,ω)-partitions （P,ω）-分区的加权Murnaghan-Nakayama规则

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2026-01-12 DOI: 10.1016/j.ejc.2025.104332

Per Alexandersson , Olivia Nabawanda

The

(P, ω)

-partition generating function

K_{(P, ω)} (x)

is a quasisymmetric function obtained from a labeled poset. Recently, Liu and Weselcouch gave a formula for the coefficients of

K_{(P, ω)} (x)

when expanded in the quasisymmetric power sum function basis. This formula generalizes the classical Murnaghan–Nakayama rule for Schur functions.

We extend this result to weighted

(P, ω)

-partitions and provide a short combinatorial proof, avoiding the Hopf algebra machinery used by Liu–Weselcouch.

（P,ω）分块生成函数K(P,ω)(x)是由标记偏序集得到的拟对称函数。最近，Liu和Weselcouch给出了K(P,ω)(x)在拟对称幂和函数基上展开时的系数公式。这个公式推广了Schur函数的经典Murnaghan-Nakayama规则。我们将这个结果推广到加权（P,ω）分区，并提供了一个简短的组合证明，避免了Liu-Weselcouch使用的Hopf代数机制。

引用次数: 0

Perfect matroids over skew hyperfields 倾斜超场上的完美拟阵

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2026-01-09 DOI: 10.1016/j.ejc.2025.104327

Nathan Bowler , Rudi Pendavingh

A hyperfield

H

is stringent if

a ⊞ b

is a singleton unless

a = - b

, for all

a, b \in H

. By a construction of Marc Krasner, each valued field gives rise to a stringent hyperfield. We show that if

H

is a stringent skew hyperfield, then weak matroids over

H

are strong matroids over

H

. Also, we present vector axioms for matroids over stringent skew hyperfields which generalize the vector axioms for oriented matroids and valuated matroids.

对于所有的A，b∈H，如果A + b是单态，则超场H是严格的，除非A = - b。通过Marc Krasner的构造，每个有值场都会产生一个严格的超场。我们证明了如果H是一个严格的斜超场，那么H上的弱拟阵就是H上的强拟阵。同时，我们给出了严格斜超场上的拟阵的向量公理，推广了有向拟阵和赋值拟阵的向量公理。

引用次数: 0

Single-element extensions of matroids over skew tracts 斜束上拟阵的单元扩展

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2026-01-05 DOI: 10.1016/j.ejc.2025.104328

Ting Su

Matroids over skew tracts provide an algebraic framework simultaneously generalizing the notions of linear subspaces, matroids, oriented matroids, phased matroids, and some other “matroids with extra structure”. A single-element extension of a matroid

M

over a skew tract

T

is a matroid

\tilde{M}

over

T

obtained from

M

by adding one more element. Crapo characterized single-element extensions of ordinary matroids, and Las Vergnas characterized single-element extensions of oriented matroids, in terms of single-element extensions of their rank 2 contractions. The results of Crapo and Las Vergnas do not generalize to matroids over skew tracts, but we will show a necessary and sufficient condition on skew tracts, called Pathetic Cancellation, such that the result can generalize to weak matroids over skew tracts.

Stringent skew hyperfields are a special case of skew tracts which behave in many ways like skew fields. We find a characterization of single-element extensions of strong matroids over stringent skew hyperfields.

斜束上的拟阵提供了一个代数框架，同时推广了线性子空间、拟阵、定向拟阵、相拟阵和其他一些“带额外结构的拟阵”的概念。斜束T上的矩阵M的单元素扩展是由M再加一个元素得到的矩阵M ~ / T。Crapo用普通拟阵的单元扩展来表示普通拟阵，Las Vergnas用定向拟阵的2阶缩缩的单元扩展来表示定向拟阵的单元扩展。Crapo和Las Vergnas的结果不能推广到偏束上的拟阵，但我们将给出一个关于偏束的充要条件，称为可悲抵消，使得结果可以推广到偏束上的弱拟阵。严格倾斜超场是倾斜束的一种特殊情况，它在许多方面表现得像倾斜场。我们得到了强拟阵在严格偏超场上的单元扩展的一个刻划。

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引用次数: 0

Recovery of cyclic words by their subwords 根据循环词的子词恢复循环词

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2026-01-02 DOI: 10.1016/j.ejc.2025.104329

Sergey Luchinin , Svetlana Puzynina , Michaël Rao

The problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in order to uniquely identify a word. In this paper we show that a cyclic word on a binary alphabet can be reconstructed by its scattered subwords of length

\frac{3}{4} n + 4

, and for each

n

one can find two cyclic words of length

n

which have the same set of scattered subwords of length

\frac{3}{4} n - \frac{3}{2}

从词的子词重建词的问题涉及确定所需的最小信息量，例如特定长度的分散子词的多集或来自给定集的分散子词的频率，以便唯一地标识一个词。本文证明了二进制字母表上的一个循环字可以用它的长度为34n+4的分散子字来重构，并且对于每一个n，可以找到两个长度为n的循环字，它们具有相同的长度为34n−32的分散子字集。

引用次数: 0

A note on the maximum diversity of intersecting families in the symmetric group 对称群中相交族的最大多样性的注记

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2025-12-31 DOI: 10.1016/j.ejc.2025.104331

Jian Wang , Jimeng Xiao

Let

S_{n}

be the symmetric group on the set

[n] ≔ {1, 2, \dots, n}

. A family

F \subset S_{n}

is called intersecting if for every

σ, π \in F

there exists some

i \in [n]

such that

σ (i) = π (i)

. Deza and Frankl proved that the largest intersecting family of permutations is the full star, that is, the collection of all permutations with a fixed position. The diversity of an intersecting family

F

is defined as the minimum number of permutations in

F

, whose deletion results in a star. In the present paper, by applying the spread approximation method developed recently by Kupavskii and Zakharov, we prove that for

n \geq 500

the diversity of an intersecting subfamily of

S_{n}

is at most

(n - 3) (n - 3)!

, which is best possible.

设Sn是集合[n]上的对称群，其中包括{1,2，…，n}。如果对于每一个σ，π∈F存在某个i∈[n]使得σ(i)=π(i)，则称族F∧Sn相交。Deza和Frankl证明了最大的相交排列族是全星形排列，即所有位置固定的排列的集合。交叉家族F的多样性定义为F中最小排列数，其缺失导致星形。本文利用Kupavskii和Zakharov最近提出的扩展逼近方法，证明了当n≥500时，Sn的相交子族的分集不超过（n−3）（n−3）！这是最好的选择。

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引用次数: 0

Maximizing the number of rational-value sums or zero-sums 使有理值和或零和的数目最大化

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2025-12-30 DOI: 10.1016/j.ejc.2025.104324

Benjamin Móricz , Zoltán Lóránt Nagy

What is the maximum number of

r

-term sums admitting rational values in

n

-element sets of irrational numbers? We determine the maximum when

r < 4

r \geq n / 2

and also in case when we drop the condition on the number of summands. It turns out that the

r

-term sum problem is equivalent to determine the maximum number of

r

-term zero-sum subsequences in

n

-element sequences of integers, which can be seen as a variant of the famous Erdős–Ginzburg–Ziv theorem.

n元素无理数集合中允许有理数的r项和的最大个数是多少？我们在r<；4或r≥n/2时确定最大值，也在放弃求和个数的条件时确定最大值。事实证明，r项和问题等价于确定n元素整数序列中r项零和子序列的最大个数，这可以看作是著名的Erdős-Ginzburg-Ziv定理的一个变体。

引用次数: 0

On the minimum spanning tree distribution in grids 网格中最小生成树分布的研究

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2025-12-27 DOI: 10.1016/j.ejc.2025.104325

Kristopher Tapp

We study the minimum spanning tree distribution on the space of spanning trees of the

n

-by-

n

grid for large

n

. We establish bounds on the decay rates of the probability of the most and the least probable spanning trees as

n \to \infty

, and we develop general tools for studying the decay rates of spanning tree families.

我们研究了n × n网格中生成树在n大时的最小生成树分布。我们建立了n→∞时最可能和最小可能生成树的概率衰减率的界，并开发了研究生成树族衰减率的通用工具。

引用次数: 0

Acyclic subgraphs of digraphs with high chromatic number 高色数有向图的无环子图

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2025-12-26 DOI: 10.1016/j.ejc.2025.104323

Raphael Yuster

For a digraph

G

, let

f (G)

be the maximum chromatic number of an acyclic subgraph of

G

. For an

n

-vertex digraph

G

it is proved that

f (G) \geq n^{5 / 9 - o (1)} s^{- 14 / 9}

where

s

is the bipartite independence number of

G

, i.e., the largest

s

for which there are two disjoint

s

-sets of vertices with no edge between them. This generalizes a result of Fox, Kwan and Sudakov, who proved this for the case

s = 0

(i.e., tournaments and semicomplete digraphs). Consequently, if

s = n^{o (1)}

, then

f (G) \geq n^{5 / 9 - o (1)}

which polynomially improves the folklore bound

f (G) \geq n^{1 / 2 - o (1)}

. As a corollary, with high probability, all orientations of the random

n

-vertex graph with edge probability

p = n^{- o (1)}

(in particular, constant

p

, hence almost all

n

-vertex graphs) satisfy

f (G) \geq n^{5 / 9 - o (1)}

. Our proof uses a theorem of Gallai and Milgram that together with several additional ideas, essentially reduces to the proof of Fox, Kwan and Sudakov.

对于有向图G，设f(G)为G的无环子图的最大色数。对于n顶点有向图G，证明了f(G)≥n5/9−0 (1)s−14/9，其中s为G的二部无关数，即存在两个不相交的无边的顶点s集的最大s。这推广了Fox， Kwan和Sudakov的结果，他们在s=0的情况下证明了这一点（即比赛和半完全有向图）。因此，如果s=no(1)，则f(G)≥n5/9−o(1)，这多项式地改善了民间传说界f(G)≥n1/2−o(1)。作为一个推论，在高概率下，边概率p=n−o(1)的随机n顶点图（特别是常数p，因此几乎所有n顶点图）的所有方向都满足f(G)≥n5/9−o(1)。我们的证明使用了Gallai和Milgram的一个定理，加上一些额外的想法，本质上归结为Fox， Kwan和Sudakov的证明。

引用次数: 0

A self-conjugate partition analog of (t,t+1)-core partitions with distinct parts 具有不同部分的（t,t+1）核划分的自共轭划分模拟

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2025-12-22 DOI: 10.1016/j.ejc.2025.104322

Huan Xiong, Lihong Yang

Simultaneous core partitions have been extensively studied over the past two decades. In 2013, Amdeberhan proposed several conjectures regarding the number, the average size, and the largest size of

(t, t + 1)

-core partitions with distinct parts. These conjectures were proved and generalized by Straub, Nath-Sellers, Zaleski-Zeilberger, Xiong, Paramonov, and many other mathematicians. In this paper, we introduce a natural self-conjugate partition analog of

(t, t + 1)

-core partitions with distinct parts and derive their number, average size, and largest size.

在过去的二十年里，同步岩心分区得到了广泛的研究。Amdeberhan在2013年提出了关于（t,t+1）个具有不同部分的核分区的数量、平均大小和最大大小的几个猜想。这些猜想被Straub、Nath-Sellers、Zaleski-Zeilberger、Xiong、Paramonov和许多其他数学家证明并推广。本文引入了具有不同部分的（t,t+1）核划分的自然自共轭模拟，并导出了它们的数目、平均大小和最大大小。

引用次数: 0

A new bijective proof of the q-Pfaff–Saalschütz identity with applications to quantum groups q- pfaff - saalsch<e:1>兹恒等式的新双射证明及其在量子群中的应用

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics

Pub Date : 2025-12-22 DOI: 10.1016/j.ejc.2025.104321

Álvaro Gutiérrez , Álvaro L. Martínez , Michał Szwej , Mark Wildon

We present a combinatorial proof of the

q

-Pfaff–Saalschütz identity by a composition of explicit bijections, in which

q

-binomial coefficients are interpreted as counting subspaces of

F_{q}

-vector spaces. As a corollary, we obtain a new multiplication rule for quantum binomial coefficients and hence a new presentation of Lusztig’s integral form

U_{Z [q, q^{- 1}]} ({sl}_{2})

of the Cartan subalgebra of the quantum group

U_{q} ({sl}_{2})

利用显式双射的复合给出了q- pfaff - saalsch兹恒等式的组合证明，其中q-二项式系数被解释为fq -向量空间的计数子空间。作为推论，我们得到了量子二项式系数的一个新的乘法规则，从而得到了量子群Uq（sl2）的Cartan子代数的Lusztig积分形式UZ[q，q−1]（sl2）的一个新的表示。

引用次数: 0

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