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Three Alternating Sign Matrix Identities in Search of Bijective Proofs

✍ Scribed by David M. Bressoud

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 121 KB
Volume: 27
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0735

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✦ Synopsis

This paper highlights three known identities, each of which involves sums over alternating sign matrices. While proofs of all three are known, the only known derivations are as corollaries of difficult results. The simplicity and natural combinatorial interpretation of these identities, however, suggest that there should be direct, bijective proofs.