Richard A. Brualdi, Hwa Kyung Kim
Published 2013-09-04Version 1
In alternating sign matrices the first and last nonzero entry in each row and column is specified to be +1. Such matrices always exist. We investigate a generalization by specifying independently the sign of the first and last nonzero entry in each row and column to be either a +1 or a -1. We determine necessary and sufficient conditions for such matrices to exist.
Weighted counting of inversions on alternating sign matrices
A directed graph structure of alternating sign matrices
A poset $Φ_n$ whose maximal chains are in bijection with the $n \times n$ alternating sign matrices
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