On Refined Enumerations of Totally Symmetric Self-Complementary Plane Partitions I

Abstract

In this paper we give Pfaffian expressions and constant term identities for the enumeration problems presented by Mills, Robbins and Rumsey (“Selfcomplementary totally symmetric plane partitions” J. Combin. Theory Ser. A 42, 277–292), concerning the totally symmetric self-complementary plane partitions (TSSCPPs). We also present some new conjectures and give Pfaffian expressions for them

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