Geodesic
On self-avoiding walks on certain grids and the connective constant
Serdica Mathematical Journal, Tome 38 (2012) no. 4, pp. 615-632.

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We consider self-avoiding walks on the square grid graph. More precisely we investigate the number of walks of a fixed length on Z×{-1,0,1}. Using combinatorial arguments we derive the related generating function. We present the asymptotic estimates of the number of walks in consideration, as well as important connective constants.
Keywords: Self-Avoiding Walks 
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     title = {On self-avoiding walks on certain grids and the connective constant},
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Dangovski, Rumen. On self-avoiding walks on certain grids and the connective constant. Serdica Mathematical Journal, Tome 38 (2012) no. 4, pp. 615-632. http://geodesic.mathdoc.fr/item/SMJ2_2012_38_4_a3/