Séminaire Lotharingien de Combinatoire, B46c (2001), 11 pp.

Theresia Eisenkölbl

2-Enumerations of Halved Alternating Sign Matrices

Abstract. We compute 2-enumerations of certain halved alternating sign matrices. In one case the enumeration equals the number of perfect matchings of a halved Aztec diamond. In the other case the enumeration equals the number of perfect matchings of a halved fortress graph. Our results prove three conjectures by Jim Propp.

Received: May 18, 2001; Accepted: June 20, 2001.

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