On refined enumerations of totally symmetric self-complementary plane partitions I

2006/02/04 by Masao Ishikawa, Ishikawa, Masao
Mathematics · #05A15 #05A17 #05E05 #05E10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0602068

openalex publication_date 2006/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Symmetry Classes of Alternating Sign Matrices
• Minor summation formula and a proof of Stanley's open problem

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• (-1)-enumeration of self-complementary plane partitions
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