Abstract
We extend a previous conjecture (P Di Francesco 2004 J. Stat. Mech.: Theor. Exp. P08009) 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 1s on their top and bottom rows. This seems to indicate a deep correspondence between observables in the two models.
| Original language | English (US) |
|---|---|
| Article number | P11004 |
| Journal | Journal of Statistical Mechanics: Theory and Experiment |
| Issue number | 11 |
| DOIs | |
| State | Published - Nov 2004 |
| Externally published | Yes |
Keywords
- loop models and polymers
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty