Self-Avoiding Walks and Fibonacci Numbers

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow

Document Type

Article

Department

Mathematics (HMC)

Publication Date

11-2006

Abstract

By combinatorial arguments, we prove that the number of self-avoiding walks on the strip {0, 1} × Z is 8F_n − 4 when n is odd and is 8F_n − n when n is even. Also, when backwards moves are prohibited, we derive simple expressions for the number of length n self-avoiding walks on {0, 1} × Z, Z × Z, the triangular lattice, and the cubic lattice.

Comments

Archived with permission from the editor of the Fibonacci Quarterly.

Rights Information

© 2006 The Fibonacci Association

Recommended Citation

Benjamin, Arthur T. "Self-Avoiding Walks and Fibonacci Numbers." The Fibonacci Quarterly, Vol. 44, No. 4, pp. 330-334, November 2006.