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

Research output: Contribution to conferencePaper

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
Publication statusPublished - Dec 1 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

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities'. Together they form a unique fingerprint.

  • Cite this

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