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Full-Text Articles in Number Theory
Self-Avoiding Walks And Fibonacci Numbers, Arthur T. Benjamin
Self-Avoiding Walks And Fibonacci Numbers, Arthur T. Benjamin
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By combinatorial arguments, we prove that the number of self-avoiding walks on the strip {0, 1} × Z is 8Fn − 4 when n is odd and is 8Fn − 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.