A refined Razumov-Stroganov conjecture II
arXiv:cond-mat/0409576 · doi:10.1088/1742-5468/2004/11/P11004
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.
21 pages, 10 figures (3 in text), uses lanlmac, hyperbasics and epsf macros
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- Inhomogeneous loop models with open boundaries
- Multiply-refined enumeration of alternating sign matrices
- A doubly-refined enumeration of alternating sign matrices and descending plane partitions