2-enumerations of halved alternating sign matrices

2001/06/06 by Theresia Eisenkölbl
Mathematics · #math.CO #msc:05A15

paper · pdf

published as Séminaire Lotharingien Combin. 46, (2001), Article B46c, 11pp · 11 pages, AmS-LaTeX, uses TeXDraw

arxiv created 2001/06/06 · arxiv updated 2009/11/30

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.

Related

• More refined enumerations of alternating sign matrices
• A formula for the doubly-refined enumeration of alternating sign matrices
• Another proof of the alternating sign matrix conjecture
• The many faces of alternating-sign matrices
• Linear relations of refined enumerations of alternating sign matrices