On FPL configurations with four sets of nested arches
Statistical Mechanics
2009-11-10 v2 Mathematical Physics
Combinatorics
math.MP
Abstract
The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.
Keywords
Cite
@article{arxiv.cond-mat/0403268,
title = {On FPL configurations with four sets of nested arches},
author = {P. Di Francesco and J. -B. Zuber},
journal= {arXiv preprint arXiv:cond-mat/0403268},
year = {2009}
}
Comments
22 pages, TeX, 16 figures; a new formula for a generating function added