Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system

• Autorzy: Andrzej Chydziński , Bogdan Smołka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 05A15: Exact enumeration problems, generating functions
• 68U10: Image processing
• 82B41: Random walks, random surfaces, lattice animals, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2001
• Tom: 28
• Numer: 2
• Strony: 169-180

Daty

wydano

2001

Twórcy

autor

Andrzej Chydziński

• Department of Mathematics, Silesian Technical University, Kaszubska 23, 44-101 Gliwice, Poland

autor

Bogdan Smołka

• Department of Computer Science, Silesian Technical University, Akademicka 16, 44-101 Gliwice, Poland

Identyfikatory

DOI

10.4064/am28-2-4