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Alternating sign matrices with one -1 under vertical reflection

Pierre Lalonde
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Abstract

We define a bijection that transforms an alternating sign matrix A with one -1 into a pair (N,E) where N is a (so called) ``neutral'' alternating sign matrix (with one -1) and E is an integer. The bijection preserves the classical parameters of Mills, Robbins and Rumsey as well as three new parameters (including E). It translates vertical reflection of A into vertical reflection of N. A hidden symmetry allows the interchange of E with one of the remaining two new parameters. A second bijection transforms (N,E) into a configuration of lattice paths called ``mixed configuration''.

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Pierre Lalonde. 2004-01-25. Alternating sign matrices with one -1 under vertical reflection. https://arxiv.org/abs/math/0401339

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