2-enumerations of halved alternating sign matrices
Theresia Eisenk\"olbl (Universit\"at Wien)
TL;DR
This paper computes specific 2-enumerations of halved alternating sign matrices, linking them to perfect matchings of halved Aztec diamonds and fortress graphs, thereby proving three conjectures by Jim Propp.
Contribution
It introduces exact enumeration formulas for halved alternating sign matrices, confirming three conjectures and connecting combinatorial objects with perfect matchings.
Findings
Enumeration equals perfect matchings of halved Aztec diamond
Enumeration equals perfect matchings of halved fortress graph
Proves three conjectures by Jim Propp
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.
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Taxonomy
TopicsGraph theory and applications · Advanced Combinatorial Mathematics · Graph Labeling and Dimension Problems