English

A refined Razumov-Stroganov conjecture II

Statistical Mechanics 2011-02-16 v1 High Energy Physics - Theory Mathematical Physics Combinatorics math.MP

Abstract

We extend a previous conjecture [cond-mat/0407477] relating the Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to refined numbers of alternating sign matrices. By considering the O(1) loop model on a semi-infinite cylinder with dislocations, we obtain the generating function for alternating sign matrices with prescribed positions of 1's on their top and bottom rows. This seems to indicate a deep correspondence between observables in both models.

Keywords

Cite

@article{arxiv.cond-mat/0409576,
  title  = {A refined Razumov-Stroganov conjecture II},
  author = {P. Di Francesco},
  journal= {arXiv preprint arXiv:cond-mat/0409576},
  year   = {2011}
}

Comments

21 pages, 10 figures (3 in text), uses lanlmac, hyperbasics and epsf macros

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