Combinatorics and Graph Theory

   

Enumeration of Self-Avoiding Walks in a Lattice

Authors: Tom Harvey

A self-avoiding walk (SAW) is a path on a lattice that does not pass through the same point more than once. We develop a method for enumerating self-avoiding walks in a lattice by decomposing them into smaller pieces called tiles, solving particular cases on the square, triangular and cubic lattices. We also show that enumeration of SAWs in a lattice is related to enumeration of edge-connected shapes, for example polyominoes.

Comments: 12 Pages.

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Submission history

[v1] 2013-05-06 20:09:16

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