Poincaré polynomial at - 1 associated with a Young diagram of three rows

Ronit Mansour

doi:10.1007/s10801-022-01142-1

Poincaré polynomial at - 1 associated with a Young diagram of three rows

Ronit Mansour

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we give an explicit formula for the Poincaré polynomial P_λ(x) for the Betti numbers of the Springer fibers over nilpotent elements in gl_n(C) of Jordan form λ= abc with a≥ b≥ c≥ 0 at x= - 1. In particular, we introduce λ-vacillating diagrams and show that P_ab(- 1) is equal to the number of restricted Dyck paths.

Original language	English
Pages (from-to)	1011-1021
Number of pages	11
Journal	Journal of Algebraic Combinatorics
Volume	56
Issue number	4
DOIs	https://doi.org/10.1007/s10801-022-01142-1
State	Published - Dec 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Dyck paths
Poincaré polynomial
λ-vacillating diagrams

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.1007/s10801-022-01142-1

Cite this

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abstract = "In this paper, we give an explicit formula for the Poincar{\'e} polynomial Pλ(x) for the Betti numbers of the Springer fibers over nilpotent elements in gln(C) of Jordan form λ= abc with a≥ b≥ c≥ 0 at x= - 1. In particular, we introduce λ-vacillating diagrams and show that Pab(- 1) is equal to the number of restricted Dyck paths.",

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Poincaré polynomial at - 1 associated with a Young diagram of three rows

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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