On Zeilberger's Constant Term for Andrews' TSSCPP Theorem

Details On Zeilberger's Constant Term for Andrews' TSSCPP Theorem On Zeilberger's Constant Term for Andrews' TSSCPP Theorem

2011-06-24

arxiv.org/abs/1106.4870v1

Electronic Journal of Combinatorics, 18 (2) (2011) P11

Mathematics

Combinatorics

13 pages, two comments from Krattenhaler are added at the end of the file

Scientific paper

This paper studies Zeilberger's two prized constant term identities. For one of the identities, Zeilberger asked for a simple proof that may give rise to a simple proof of Andrews theorem for the number of totally symmetric self complementary plane partitions. We obtain an identity reducing a constant term in $2k$ variables to a constant term in $k$ variables. As applications, Zeilberger's constant terms are converted to single determinants. The result extends for two classes of matrices, the sum of all of whose full rank minors is converted to a single determinant. One of the prized constant term problems is solved, and we give a seemingly new approach to Macdonald's constant term for root system of type BC.

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