Geodesic
Self-avoiding walks on the lattice ${\Bbb Z}^2$ with the 8-neighbourhood system
Andrzej Chydzi/nski 1   ; Bogdan Smo/lka 2
1 Department of Mathematics Silesian Technical University Kaszubska 23 44-101 Gliwice, Poland
2 Department of Computer Science Silesian Technical University Akademicka 16 44-101 Gliwice, Poland
Applicationes Mathematicae, Tome 28 (2001) no. 2, pp. 169-180 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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This paper deals with the properties of self-avoiding walks defined on the lattice with the 8-neighbourhood system. We compute the number of walks, bridges and mean-square displacement for $N=1$ through 13 ($N$ is the number of steps of the self-avoiding walk). We also estimate the connective constant and critical exponents, and study finite memory and generating functions. We show applications of this kind of walk. In addition, we compute upper bounds for the number of walks and the connective constant.
DOI : 10.4064/am28-2-4
Keywords: paper deals properties self avoiding walks defined lattice neighbourhood system compute number walks bridges mean square displacement through number steps self avoiding walk estimate connective constant critical exponents study finite memory generating functions applications kind walk addition compute upper bounds number walks connective constant

Andrzej Chydzi/nski  1   ; Bogdan Smo/lka  2

1 Department of Mathematics Silesian Technical University Kaszubska 23 44-101 Gliwice, Poland
2 Department of Computer Science Silesian Technical University Akademicka 16 44-101 Gliwice, Poland 
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Andrzej Chydzi/nski; Bogdan Smo/lka. Self-avoiding walks on the lattice ${\Bbb Z}^2$
with the 8-neighbourhood system. Applicationes Mathematicae, Tome 28 (2001) no. 2, pp. 169-180. doi: 10.4064/am28-2-4

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