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 (``Self-complementary 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.

39 pages, 2 figures

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Cited by in corpus (5)

• Multiply-refined enumeration of alternating sign matrices
• A doubly-refined enumeration of alternating sign matrices and descending plane partitions
• Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions
• On some polynomials enumerating Fully Packed Loops configurations, evaluation at negative values
• Higher Spin Alternating Sign Matrices