Abstract:
Kuperberg showed 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
bijective correspondence with half-turn-symmetric alternating-sign matrices
of odd order. The partition function of this model is expressed via the above
factors. We find the contributions to the partition function that correspond
to the alternating-sign matrices having $1$ or $-1$ as the central entry and
establish the related enumerations.