Lattice animals on a staircase and generalized Fibonacci numbers
Statistical Mechanics
2007-05-23 v2
Abstract
We study the statistics of column-convex lattice animals generated by the stacking of squares on a staircase with step height p. We calculate the number of animals with area k living on l stairs. The total number of animals with area k is given by the generalized Fibonacci number F_p(k). Exact results for the mean length and mean height of animals with area k are also obtained and we examine their asymptotic behaviour.
Keywords
Cite
@article{arxiv.cond-mat/0106595,
title = {Lattice animals on a staircase and generalized Fibonacci numbers},
author = {L. Turban},
journal= {arXiv preprint arXiv:cond-mat/0106595},
year = {2007}
}
Comments
10 pages, 1 figure, LaTeX2e, epsf+Elsevier macro, minor correction