arXiv:math-ph/0605004 · Journal of Statistical Mechanics Theory and Experiment

Bethe roots and refined enumeration of alternating-sign matrices

A. V. Razumov, Yu. G. Stroganov

Published Jul 13, 2006• 18 citations

Abstract

The properties of the most probable ground state candidate for the XXZ spin chain with the anisotropy parameter equal to −1/2 and an odd number of sites is considered. Some linear combinations of the components of the state considered, divided by the maximal component, coincide with the elementary symmetric polynomials in the corresponding Bethe roots. It is proved that these polynomials are equal to the numbers providing the refined enumeration of the alternating-sign matrices of order M +1 divided by the total number of the alternating-sign matrices of order M , for the chain of length 2 M +1.

DOI: 10.1088/1742-5468/2006/07/p07004

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