德凡特和克拉维茨关于人字形环路长度定理的简明证明

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2024-01-02 DOI:10.1007/s00026-023-00681-z

Qiuyu Ren, Shengtong Zhang

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引用次数: 0

摘要

我们为迪凡特和克拉维茨的定理提供了一个更简短的证明，即人字桥环路的长度与 4 模 8 全等。我们新颖的想法是考虑在半平面区域内游走的人头桥路径的长度模数 8。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A Succinct Proof of Defant and Kravitz’s Theorem on the Length of Hitomezashi Loops

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A Succinct Proof of Defant and Kravitz’s Theorem on the Length of Hitomezashi Loops

We provide a much shorter proof of Defant and Kravitz’s theorem that the length of Hitomezashi loops is congruent to 4 modulo 8. Our novel idea is to consider the length module 8 for Hitomezashi paths that take an excursion in a half-plane region.

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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