Dyck paths and a bijection for multisets of hook numbers

Ian Goulden; Alexander Yong

doi:10.1016/S0012-365X(01)00356-9

Dyck paths and a bijection for multisets of hook numbers

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

Abstract

We give a bijective proof of a result of Regev and Vershik (Electron J. Combin. 4 (1997) R22) on the equality of two multisets of hook numbers of certain skew-Young diagrams. The bijection is given in terms of Dyck paths, a particular type of lattice path. It is extended to also prove a recent, more refined result of Regev (European J. Combin. 21 (2000) 959), which concerns a special class of skew diagrams.

Original language	English (US)
Pages (from-to)	153-164
Number of pages	12
Journal	Discrete Mathematics
Volume	254
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(01)00356-9
State	Published - Jun 10 2002
Externally published	Yes

Keywords

Bijection
Dyck path
Hook number
Projective representation

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Online availability

10.1016/S0012-365X(01)00356-9

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title = "Dyck paths and a bijection for multisets of hook numbers",

abstract = "We give a bijective proof of a result of Regev and Vershik (Electron J. Combin. 4 (1997) R22) on the equality of two multisets of hook numbers of certain skew-Young diagrams. The bijection is given in terms of Dyck paths, a particular type of lattice path. It is extended to also prove a recent, more refined result of Regev (European J. Combin. 21 (2000) 959), which concerns a special class of skew diagrams.",

keywords = "Bijection, Dyck path, Hook number, Projective representation",

author = "Ian Goulden and Alexander Yong",

note = "Funding Information: This work was supported by the Natural Sciences and Engineering Research Council of Canada, through a grant to IG, and a PGSA to AY. We thank a referee of an earlier version of this paper for informing us about references [3–5], and suggesting that the methods of Sections 1 and 2 could be extended to treat the projective case. This led to the addition of Section 3 in the 7n al version of the paper.",

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AU - Goulden, Ian

AU - Yong, Alexander

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PY - 2002/6/10

Y1 - 2002/6/10

N2 - We give a bijective proof of a result of Regev and Vershik (Electron J. Combin. 4 (1997) R22) on the equality of two multisets of hook numbers of certain skew-Young diagrams. The bijection is given in terms of Dyck paths, a particular type of lattice path. It is extended to also prove a recent, more refined result of Regev (European J. Combin. 21 (2000) 959), which concerns a special class of skew diagrams.

AB - We give a bijective proof of a result of Regev and Vershik (Electron J. Combin. 4 (1997) R22) on the equality of two multisets of hook numbers of certain skew-Young diagrams. The bijection is given in terms of Dyck paths, a particular type of lattice path. It is extended to also prove a recent, more refined result of Regev (European J. Combin. 21 (2000) 959), which concerns a special class of skew diagrams.

KW - Bijection

KW - Dyck path

KW - Hook number

KW - Projective representation

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Dyck paths and a bijection for multisets of hook numbers

Abstract

Keywords

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