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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish
Title of host publicationFPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics
Publication statusPublished - 2007
Externally publishedYes
Event19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China
Duration: Jul 2 2007Jul 6 2007

Other

Other19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07
CountryChina
CityTianjin
Period7/2/077/6/07

Fingerprint

Plane Partitions
Constant term
Enumeration
Alternating Sign Matrices
Pfaffian
Invariant
Flip
Involution
Determinant
Vertical

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

Ishikawa, M. (2007). Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities. In FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics

Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities. / Ishikawa, Masao.

FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics. 2007.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ishikawa, M 2007, Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities. in FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics. 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07, Tianjin, China, 7/2/07.
Ishikawa M. Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities. In FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics. 2007
Ishikawa, Masao. / Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities. FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics. 2007.
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