content:mathematics:self_avoiding_walks

# Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

# Self avoiding walks

In mathematics, a *Self-Avoiding Walk* (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. (see Wikipedia )

The question of how many possible *n*-step SAWs are available on any given lattice is an open problem. It's possible to calculate the upper and lower bounds for the number of walks :

[โฆ] but still the only known way to get an exact tally is to actually trace out all then-step walks and count them.

Source : American Scientist,Volume 86, Number 4, pages 314โ319

For a recent study into a possible mathematical model, see : Theophilus Agama (2021) On a function modeling an l-step self avoiding walk, *AKCE International Journal of Graphs and Combinatorics.*

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