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Alternating sign matrices with one −1 under vertical reflection

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Publication Date
Volume
113
Issue
6
Identifiers
DOI: 10.1016/j.jcta.2005.09.002
Keywords
  • Alternating Sign Matrices
  • Mixed Configurations
  • Lattice Paths
  • Path Duality

Abstract

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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