Enumerating up-side self-avoiding walks on integer lattices (Q1379176)
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scientific article; zbMATH DE number 1120245
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Enumerating up-side self-avoiding walks on integer lattices |
scientific article; zbMATH DE number 1120245 |
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Enumerating up-side self-avoiding walks on integer lattices (English)
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22 February 1998
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Summary: A self-avoiding walk (saw) is a path on a lattice that does not pass through the same point twice. Though mathematicians have studied saws for over fifty years, the number of \(n\)-step saws is unknown. This paper examines a special case of this problem, finding the number of \(n\)-step ``up-side'' saws (ussaws), saws restricted to moving up and sideways. It presents formulas for the number of \(n\)-step ussaws on various lattices, found using generating functions with decomposition and recursive methods.
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self-avoiding walk
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lattice
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generating functions
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