Schur function identities and hook length posets

Masao Ishikawa, Hiroyuki Tagawa

Research output: Contribution to conferencePaper

2 Citations (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
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

  • 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

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  • Cite this

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