====== 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 [[https://en.wikipedia.org/wiki/Self-avoiding_walk|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 :

>[...] but still the only known way to get an exact tally is to actually trace out all the //n//-step walks and count them.\\ \\ Source : [[http://bit-player.org/wp-content/extras/bph-publications/AmSci-1998-07-Hayes-self-avoidance.pdf|American Scientist]] //,// Volume 86, Number 4, pages 314–319

For a recent study into a possible mathematical model, see : Theophilus Agama (2021) [[https://www.tandfonline.com/doi/full/10.1080/09728600.2021.1988831|On a function modeling an l-step self avoiding walk]], //AKCE International Journal of Graphs and Combinatorics.//