A lattice point counting approach for the study of the number of self-avoiding walks on ℤ^d

2025/04/17 by Lazar, Youssef
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2504.13093

Abstract

We reduce the problem of counting self-avoiding walks in the square lattice to a problem of counting the number of integral points in multidimensional domains. We obtain an asymptotic estimate of the number of self-avoiding walks of length n in the square lattice. This new formalism gives a natural and unified setting in order to study the properties of the number of self-avoiding walks in the lattice ℤ^d of any dimension d≥ 2.

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