Schur function identities and hook length posets

Masao Ishikawa; Hiroyuki Tagawa

Schur function identities and hook length posets

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

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 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

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

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title = "Schur function identities and hook length posets",

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.",

keywords = "D-complete posets, Hook-length property, Lattice path method, Minor summation formula, Partially ordered sets, Pfaffians, Schur functions",

author = "Masao Ishikawa and Hiroyuki Tagawa",

year = "2007",

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language = "English",

note = "19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 ; Conference date: 02-07-2007 Through 06-07-2007",

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AU - Ishikawa, Masao

AU - Tagawa, Hiroyuki

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

KW - D-complete posets

KW - Hook-length property

KW - Lattice path method

KW - Minor summation formula

KW - Partially ordered sets

KW - Pfaffians

KW - Schur functions

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M3 - Paper

AN - SCOPUS:84860754090

T2 - 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07

Y2 - 2 July 2007 through 6 July 2007

ER -

Schur function identities and hook length posets

Abstract

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Keywords

ASJC Scopus subject areas

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