  It was shown by Kuperberg that the partition function of the square-ice model
related to the quarter-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 the quarter-turn symmetric alternating-sign
matrices of odd order, and show that the partition function of this model can
be also written in a similar way. This allows to prove, in particular, the
conjectures by Robbins related to the enumeration of the quarter-turn symmetric
alternating-sign matrices.
