Fixed-boundary octagonal random tilings: a combinatorial approach

Details Fixed-boundary octagonal random tilings: a combinatorial approach Fixed-boundary octagonal random tilings: a combinatorial approach

2000-04-10

arxiv.org/abs/cond-mat/0004145v2

Physics

Condensed Matter

Statistical Mechanics

36 pages, LaTeX, to appear in J. Stat. Phys (Jan. 2001)

Scientific paper

Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus generalizing previous results on the more restricted class of codimension-one tilings. In particular this method gives access to counting formulas, which are directly related to questions of entropy in these statistical systems. Methods and tools from the field of enumerative combinatorics are used.

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