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2018 Counting all self-avoiding walks on a finite lattice strip of width one and two
M.A. Nyblom
Rocky Mountain J. Math. 48(2): 573-605 (2018). DOI: 10.1216/RMJ-2018-48-2-573

Abstract

In this paper, a closed-form expression for counting all SAWs, irrespective of length, but restricted to the finite lattice strip $\{ -a,\ldots ,0,\ldots ,b\}\times \{0,1\}$, shall be obtained in terms of the non-negative integer parameters $a$ and $b$. In addition, the argument used to prove this result will be extended to establish an enumerating formula for counting all SAWs, irrespective of length, but restricted to the half-finite lattice strip of width two $\{ 0,1,\ldots ,n\}\times \{ 0,1,2\}$, in terms of $n$.

Citation

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M.A. Nyblom. "Counting all self-avoiding walks on a finite lattice strip of width one and two." Rocky Mountain J. Math. 48 (2) 573 - 605, 2018. https://doi.org/10.1216/RMJ-2018-48-2-573

Information

Published: 2018
First available in Project Euclid: 4 June 2018

zbMATH: 1388.05015
MathSciNet: MR3809156
Digital Object Identifier: 10.1216/RMJ-2018-48-2-573

Subjects:
Primary: 05A15
Secondary: 05C30

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 2 • 2018
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