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December 2020 Counting all unfolded self-avoiding walks on a finite lattice strip of width three
Michael A. Nyblom
Rocky Mountain J. Math. 50(6): 2179-2197 (December 2020). DOI: 10.1216/rmj.2020.50.2179

Abstract

By extending the method of the author’s earlier paper, a purely recursive approach is devised for counting the total number of unfolded self-avoiding walks terminating along the line x=n, within the finite lattice strip {0,1,,n}×{0,1,2,3} of width three. This approach yields a generating function for the sequence of numbers just described, without the need for any exact enumeration, usually entailed with an application of the transfer matrix algorithm. As a result of determining this generating function, the total number of unfolded walks within the lattice strip can then be easily computed.

Citation

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Michael A. Nyblom. "Counting all unfolded self-avoiding walks on a finite lattice strip of width three." Rocky Mountain J. Math. 50 (6) 2179 - 2197, December 2020. https://doi.org/10.1216/rmj.2020.50.2179

Information

Received: 17 December 2018; Revised: 23 February 2020; Accepted: 16 March 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.2179

Subjects:
Primary: 05A15
Secondary: 05C30

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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