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.
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