Some results for directed lattice walkers in a strip

Abstract : 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.
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Cyril Banderier and Christian Krattenthaler. Discrete Random Walks, DRW'03, 2003, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), pp.27-38, 2003, DMTCS Proceedings
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Yao-Ban Chan, Anthony J. Guttmann. Some results for directed lattice walkers in a strip. Cyril Banderier and Christian Krattenthaler. Discrete Random Walks, DRW'03, 2003, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), pp.27-38, 2003, DMTCS Proceedings. 〈hal-01183936〉

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