On fully packed loop configurations with four sets of nested arches

P. Di Francesco, J. B. Zuber

Research output: Contribution to journalArticlepeer-review

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 re-expression in terms of non-intersecting lines, the Lindström-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.

Original languageEnglish (US)
Article numberP06005
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number6
DOIs
StatePublished - Jun 2004
Externally publishedYes

Keywords

  • loop models and polymers
  • rigorous results in statistical mechanics
  • topology and combinatorics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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