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{\bf Guoce Xin}
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{\bf On Zeilberger's Constant Term for Andrews' TSSCPP Theorem}
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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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