Step-constrained self-avoiding walks on finite grids

Belbachir, Hacène and Major, László and Németh, László and Szalay, László (2026) Step-constrained self-avoiding walks on finite grids. JOURNAL OF COMBINATORIAL THEORY SERIES A, 218. ISSN 0097-3165

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Abstract

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.

Tudományterület / tudományág

natural sciences > mathematics and computer sciences

Faculty

Not relevant

Institution

Soproni Egyetem

Item Type:	Article
SWORD Depositor:	Teszt Sword
Depositing User:	Csaba Horváth
Identification Number:	MTMT:36329342
Date Deposited:	18 Sep 2025 10:24
Last Modified:	18 Sep 2025 10:24
URI:	http://publicatio.uni-sopron.hu/id/eprint/3733

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