Step-constrained self-avoiding walks on finite grids

Belbachir, Hacène és Major, László és Németh, László és 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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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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természettudományok > matematika- és számítástudományok

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Mű tipusa:	Cikk
SWORD Depositor:	Teszt Sword
Felhasználó:	Csaba Horváth
A mű MTMT azonosítója:	MTMT:36329342
Dátum:	18 Szep 2025 10:24
Utolsó módosítás:	18 Szep 2025 10:24
URI:	http://publicatio.uni-sopron.hu/id/eprint/3733

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