Izergin-Korepin determinant reloaded

Abstract

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.

14 pages, 2 figures

References in corpus (4)

• Another proof of the alternating sign matrix conjecture
• Proof of the Refined Alternating Sign Matrix Conjecture
• A new way to deal with Izergin-Korepin determinant at root of unity
• 3-enumerated alternating sign matrices

Cited by in corpus (12)

• Enumerations of half-turn symmetric alternating-sign matrices of odd order
• Diagonally and antidiagonally symmetric alternating sign matrices of odd order
• Multiply-refined enumeration of alternating sign matrices
• Enumeration of quarter-turn symmetric alternating-sign matrices of odd order
• A new representation for the partition function of the six vertex model with domain wall boundaries
• Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
• Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions
• Multiple integral formula for the off-shell six vertex scalar product
• Gaudin functions, and Euler-Poincaré characteristics
• On refined enumerations of totally symmetric self-complementary plane partitions I
• Studies in Integrable Quantum Lattice Models and Classical Hierarchies
• Three-coloring statistical model with domain wall boundary conditions. II. Trigonometric limit