大型$$p$$ -Core $$p'$$ -加性残差图上的分区和行走

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2022-11-24 DOI:10.1007/s00026-022-00622-2

Eoghan McDowell

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引用次数: 1

摘要

本文研究了既没有可被\（p\）整除的部分长度也没有钩长度的分区，称为\（p \）-core\（p'\）-分区。我们证明了最大的\（p\）-核心\（p'\）-分区对应于具有顶点\（0，1，\ldots，p-1\）和通过加法模\（p\\）定义的标记边的图上的最长走。我们还展示了一个大\（p\）-核\（p'\）-分区的显式族，给出了最大此类分区大小的下界，其程度与McSpirit和Ono发现的上界相同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Large $p$-Core $p'$-Partitions and Walks on the Additive Residue Graph$

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Large $p$-Core $p'$-Partitions and Walks on the Additive Residue Graph

This paper investigates partitions which have neither parts nor hook lengths divisible by $p$, referred to as $p$-core $p'$-partitions. We show that the largest $p$-core $p'$-partition corresponds to the longest walk on a graph with vertices $\{0, 1, \ldots , p-1\}$ and labelled edges defined via addition modulo $p$. We also exhibit an explicit family of large $p$-core $p'$-partitions, giving a lower bound on the size of the largest such partition which is of the same degree as the upper bound found by McSpirit and Ono.

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来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches