Schur function identities and hook length posets

Masao Ishikawa, Hiroyuki Tagawa

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

1 Citation (Scopus)

Abstract

In this paper we find new classes of posets which generalize the d-complete posets. In fact the d-complete posets are classified into 15 irreducible classes in the paper "Dynkin diagram classification of λ-minuscule Bruhat lattices and of d-complete posets" (J. Algebraic Combin. 9 (1999), 61 - 94) by R. A. Proctor. Here we present six new classes of posets of hook-length property which generalize the 15 irreducible classes. Our method to prove the hook-length property is based on R. P. Stanley's (P,ω)- partitions and Schur function identities.

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

Schur Functions
Poset
Dynkin Diagram
Generalise
Partition Function
Class

Keywords

  • D-complete posets
  • Hook-length property
  • Lattice path method
  • Minor summation formula
  • Partially ordered sets
  • Pfaffians
  • Schur functions

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Ishikawa, M., & Tagawa, H. (2007). Schur function identities and hook length posets. In FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics

Schur function identities and hook length posets. / Ishikawa, Masao; Tagawa, Hiroyuki.

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

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

Ishikawa, M & Tagawa, H 2007, Schur function identities and hook length posets. 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, Tagawa H. Schur function identities and hook length posets. In FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics. 2007
Ishikawa, Masao ; Tagawa, Hiroyuki. / Schur function identities and hook length posets. FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics. 2007.
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