Izergin-Korepin determinant reloaded

Details Izergin-Korepin determinant reloaded Izergin-Korepin determinant reloaded

2004-09-27

arxiv.org/abs/math-ph/0409072v1

Physics

Mathematical Physics

14 pages, 2 figures

Scientific paper

We consider the Izergin-Korepin determinant [1] together with another determinant which was invented by Kuperberg [2]. He used these determinants to prove a formula for the total number of half-turn symmetric alternating sign matrices of even order conjectured by Robbins [3]. By developing further the method that was described in our previous paper [4], we obtain a closed nonlinear recurrence system for these determinants. It can be used in various ways. For example, in this paper, we obtain formula (29) for the refined enumeration of half-turn symmetric alternating sign matrices of even order.

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