Using a transfer matrix method, we present some results for directed lattice walkers in a horizontal strip of finite width. Some cases with two walkers in a small width are solved exactly, as are a couple of cases with vicious walkers in a small width; a conjecture is made for a case with three walkers. We also derive the general transfer matrix for two walkers. Lastly, we examine the dependence of the growth constant on the width and friendliness.

Source : oai:HAL:hal-01183936v1

Volume: DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)

Section: Proceedings

Published on: January 1, 2003

Submitted on: May 10, 2017

Keywords: vicious walkers,friendly walkers,transfer matrix,walkers in a strip,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]

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