Lattice animals on a staircase and generalized Fibonacci numbers

2001/06/28 by L Turban, L. Turban, Turban, L. · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #FOS: Physical sciences #Quasicrystal Structures and Properties #Statistical Mechanics (cond-mat.stat-mech) #Supramolecular Self-Assembly in Materials #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0106595

10 pages, 1 figure, LaTeX2e, epsf+Elsevier macro, minor correction

openalex publication_date 2001/06/28 · arxiv created 2006/10/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Generalized Heisenberg algebras andk-generalized Fibonacci numbers
• Fibonacci and Catalan Numbers Meet in Staircase Polyominoes

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