1/N phenomenon for some symmetry classes of the odd alternating sign matrices

Details 1/N phenomenon for some symmetry classes of the odd alternating sign matrices 1/N phenomenon for some symmetry classes of the odd alternating sign matrices

2008-07-16

arxiv.org/abs/0807.2520v1

Physics

Mathematical Physics

3 pages

Scientific paper

We consider the alternating sign matrices of the odd order that have some kind of central symmetry. Namely, we deal with matrices invariant under the half-turn, quarter-turn and flips in both diagonals. In all these cases, there are two natural structures in the centre of the matrix. For example, for the matrices invariant under the half-turn the central element is equal $\pm 1$. It was recently found that $A^+_{HT}(2m+1)/A^-_{HT}(2m+1)$=(m+1)/m. We conjecture that similar very simple relations are valid in the two remaining cases.

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