Enumerations of half-turn symmetric alternating-sign matrices of odd order

Abstract

It was shown by Kuperberg that the partition function of the square-ice model related to half-turn symmetric alternating-sign matrices of even order is the product of two similar factors. We propose a square-ice model whose states are in bijection with half-turn symmetric alternating-sign matrices of odd order. The partition function of the model is expressed via the above mentioned factors. The contributions to the partition function of the states corresponding to the alternating-sign matrices having 1 or -1 as the central entry are found and the related enumerations are obtained.

28 pages, 14 figures

References in corpus (2)

• Symmetry Classes of Alternating Sign Matrices
• Izergin-Korepin determinant reloaded

Cited by in corpus (16)

• On the weighted enumeration of alternating sign matrices and descending plane partitions
• On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state
• 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 doubly-refined enumeration of alternating sign matrices and descending plane partitions
• 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
• On refined enumerations of totally symmetric self-complementary plane partitions I
• Vertex Models and Spin Chains in Formulas and Pictures
• On the symmetry of the partition function of some square ice models
• 1/N phenomenon for some symmetry classes of the odd alternating sign matrices
• Three-coloring statistical model with domain wall boundary conditions. II. Trigonometric limit
• Half-turn symmetric alternating sign matrices and Tokuyama type factorisation for orthogonal group characters
• Exact asymptotics of the characteristic polynomial of the symmetric Pascal matrix
• On the link pattern distribution of quarter-turn symmetric FPL configurations