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 : 2025-08-29 DOI:10.1016/j.jcta.2025.106104

Hacène Belbachir , László Major , László Németh , László Szalay

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引用次数: 0

摘要

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。

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Step-constrained self-avoiding walks on finite grids

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.

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.