Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities

Masao Ishikawa

Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities

Research output: Contribution to conference › Paper › peer-review

Abstract

In this paper we give Pfaffian or determinant expressions, and constant term identities for the conjectures in the paper "Self-complementary totally symmetric plane partitions" (J. Combin. Theory Ser. A 42, 277-292) by Mills, Robbins and Rumsey. We also settle a weak version of Conjecture 6 in the paper, i.e., the number of shifted plane partitions invariant under a certain involution is equal to the number of alternating sign matrices invariant under the vertical flip.

Original language	English
Publication status	Published - Dec 1 2007
Externally published	Yes
Event	19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China Duration: Jul 2 2007 → Jul 6 2007

Other

Other	19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07
Country/Territory	China
City	Tianjin
Period	7/2/07 → 7/6/07

Keywords

Alternating sign matrices
Constant term identities
Determinants and Pfaffians
Plane partitions
Symmetric functions
Symmetries

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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author = "Masao Ishikawa",

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AB - In this paper we give Pfaffian or determinant expressions, and constant term identities for the conjectures in the paper "Self-complementary totally symmetric plane partitions" (J. Combin. Theory Ser. A 42, 277-292) by Mills, Robbins and Rumsey. We also settle a weak version of Conjecture 6 in the paper, i.e., the number of shifted plane partitions invariant under a certain involution is equal to the number of alternating sign matrices invariant under the vertical flip.

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KW - Constant term identities

KW - Determinants and Pfaffians

KW - Plane partitions

KW - Symmetric functions

KW - Symmetries

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ER -

Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities

Abstract

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Keywords

ASJC Scopus subject areas

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