A1 Refereed original research article in a scientific journal
Self-avoiding walks of specified lengths on rectangular grid graphs
Authors: Major, László; Németh, László; Pahikkala, Anna; Szalay, László
Publisher: Birkhauser
Publication year: 2024
Journal: Aequationes Mathematicae
Journal name in source: Aequationes Mathematicae
Volume: 98
Issue: 1
First page : 215
Last page: 239
eISSN: 1420-8903
DOI: https://doi.org/10.1007/s00010-023-00977-8
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://link.springer.com/article/10.1007/s00010-023-00977-8
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/180426856
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
The investigation of self-avoiding walks on graphs has an extensive literature. We study the notion of wrong steps of self-avoiding walks on rectangular shape n×m grids of square cells (Manhattan graphs) and examine some general and special cases. We determine the number of self-avoiding walks with one and with two wrong steps in general. We also establish some properties, like unimodality and sum of the rows of the Pascal-like triangles corresponding to the walks. We also present particular recurrence relations on the number of self-avoiding walks on the n×2 grids with any specified number of wrong steps.
Downloadable publication This is an electronic reprint of the original article. |  |
