Journal of Combinatorial Theory Series A最新文献

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IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01

引用次数: 0

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01

引用次数: 0

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01

引用次数: 0

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01

引用次数: 0

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01

引用次数: 0

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01

引用次数: 0

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2026-01-01

引用次数: 0

Mean and variance of the longest alternating subsequence in a random separable permutation 随机可分排列中最长交替子序列的均值和方差

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2025-12-31 DOI: 10.1016/j.jcta.2025.106157

Ross G. Pinsky

<div><div>A permutation is separable if it can be obtained from the singleton permutation by iterating direct sums and skew sums. Equivalently, it is separable if and only it avoids the patterns 2413 and 3142. Under the uniform probability on separable permutations of <math><mo>[</mo><mi>n</mi><mo>]</mo></math>, let the random variable <math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math> denote the length of the longest alternating subsequence. Also, let <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>+</mo><mo>,</mo><mo>−</mo></mrow></msubsup></math> denote the length of the longest alternating subsequence that begins with an ascent and ends with a descent, and define <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mo>,</mo><mo>+</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>+</mo><mo>,</mo><mo>+</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mo>,</mo><mo>−</mo></mrow></msubsup></math> similarly. By symmetry, the first two and the last two of these latter four random variables are equi-distributed. We prove that the expected value of any of these five random variables behaves asymptotically as <math><mo>(</mo><mn>2</mn><mo>−</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>)</mo><mi>n</mi><mo>≈</mo><mn>0.5858</mn><mspace></mspace><mi>n</mi></math>. We also obtain the more refined estimates that the expected value of <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>+</mo><mo>,</mo><mo>−</mo></mrow></msubsup></math> and of <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mo>,</mo><mo>+</mo></mrow></msubsup></math> is equal to <math><mo>(</mo><mn>2</mn><mo>−</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>)</mo><mi>n</mi><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>(</mo><mn>3</mn><mo>−</mo><mn>2</mn><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>)</mo><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> and that the expected value of <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>+</mo><mo>,</mo><mo>+</mo></mrow></msubsup></math> and of <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mo>,</mo><mo>−</mo></mrow></msubsup></math> is equal to <math><mo>(</mo><mn>2</mn><mo>−</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>)</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>(</mo><mn>3</mn><mo>−</mo><mn>2</mn><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>)</mo><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>. Finally, we show that the variance of any of the four random variables <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>±</mo

一个排列是可分离的，如果它能从单态排列中通过迭代直接和和和得到。同样，当且仅当它避免了模式2413和3142时，它是可分离的。在可分离排列[n]的均匀概率下，设随机变量An表示最长交替子序列的长度。同样，设An+，−表示以上升开始，以下降结束的最长交替子序列的长度，并类似地定义An−，+,An+,+,An−,−。根据对称性，后四个随机变量的前两个和后两个是等分布的。我们证明了这五个随机变量的期望值的渐近性为（2−2）n≈0.5858n。我们还得到了An+，−和An−，+的期望值等于（2−2）n−14(3−22)+o(1)和An+，+和An−，−的期望值等于（2−2）n+34(3−22)+o(1)的更精确估计。最后，我们证明了任意四个随机变量的方差An±，±的渐近表现为16−1122n≈0.2218n。

引用次数: 0

Periods of strongly connected multivariate digraphs 强连通多元有向图的周期

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2025-12-22 DOI: 10.1016/j.jcta.2025.106156

Chengyang Qian, Yaokun Wu, Yinfeng Zhu

For a positive integer t, a t-variable digraph on a set K is defined as a map f from

K^{t}

2^{K}

. Note that an ordinary digraph is a 1-variable digraph. In 2017, Wu, Xu, and Zhu proposed the study of multivariate digraphs as a qualitative counterpart of going from Markov chains to higher-order Markov chains. A fundamental parameter of any strongly connected ordinary digraph is its period. This notion extends naturally to strongly connected t-variable digraphs. Let

PS (t)

denote the set of all possible periods of strongly connected t-variable digraphs, let

g (t)

be its Frobenius number (i.e., the largest nonnegative integer not belonging to

PS (t)

), and let

n (t)

be its Sylvester number (i.e., the number of positive integers outside of

PS (t)

). In this paper, we establish new estimates for

g (t)

and

n (t)

. We also show that

PS (t) \cap {1, 2, \dots, 4 t - 1}

equals

{1, 8}

when

t \in {3, 4}

and {1} when

t \geq 5

. Although this work originated in an effort to understand qualitative higher-order Markov chains, it turns out to be closely related to two other active areas of research, partitioning a discrete box into subboxes, and restricted universal partial cycles.

对于正整数t，集合K上的t变量有向图定义为从Kt到2K的映射。注意，普通有向图是一个单变量有向图。2017年，Wu、Xu和Zhu提出了多元有向图的研究，作为从马尔可夫链到高阶马尔可夫链的定性对应物。任何强连通普通有向图的一个基本参数是它的周期。这个概念自然地扩展到强连接的t变量有向图。设PS(t)表示强连通t变量有向图的所有可能周期的集合，设g(t)为它的Frobenius数（即不属于PS(t)的最大非负整数），设n(t)为它的Sylvester数（即不属于PS(t)的正整数的个数）。本文建立了g(t)和n(t)的新估计。我们还证明了当t∈{3,4}时，PS(t)∩{1,2，…，4t−1}={1,8}，当t≥5时，p (t)∩{1}。虽然这项工作起源于理解定性高阶马尔可夫链的努力，但事实证明，它与另外两个活跃的研究领域密切相关，将离散盒划分为子盒，以及限制泛环。

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引用次数: 0

On edge-primitive Cayley graphs 在边基Cayley图上

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2025-12-22 DOI: 10.1016/j.jcta.2025.106155

Zai Ping Lu, Yue Sun

A graph is said to be edge-primitive if its automorphism group acts primitively on the edge set. In this paper, we investigate finite edge-primitive Cayley graphs of valency no less than 2. An explicit classification of such graphs is obtained in the case where the graphs admit an almost simple edge-primitive automorphism group which contains a regular subgroup on the vertices. This implies that the only edge-primitive Cayley graphs of valency at least 2 defined over simple groups are cycles with prime length and complete graphs. In addition, we also classify those edge-primitive Cayley graphs which are either 2-arc-transitive or of square-free order.

如果图的自同构群基本作用于边集，则称图为边基图。本文研究了价不小于2的有限边基Cayley图。当图承认一个几乎简单的边原自同构群，且该群在顶点上包含正则子群时，得到了这类图的显式分类。这表明在单群上定义的价至少为2的边基Cayley图只有素数长度的环和完全图。此外，我们还对2-弧传递和无平方阶的边基Cayley图进行了分类。

引用次数: 0

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