On bar lengths in partitions

Jean-Baptiste Bernard Gramain; Jørn Børling Olsson

doi:10.1017/s0013091512000387

On bar lengths in partitions

Bidragets oversatte titel: Om længder af bars i partitioner

Jean-Baptiste Bernard Gramain, Jørn Børling Olsson

Institut for Matematiske Fag

Abstract

We present, given an odd integer d, a decomposition of the multiset of bar lengths of a bar partition λ as the union of two multisets, one consisting of the bar lengths in its d -core partition c d (λ) and the other consisting of modified bar lengths in its d -quotient partition. In particular, we obtain that the multiset of bar lengths in c d (λ) is a sub-multiset of the multiset of bar lengths in λ. Also, we obtain a relative bar formula for the degrees of spin characters of the Schur extensions of _n. The proof involves a recent similar result for partitions, proved by Bessenrodt and the authors.

Bidragets oversatte titel	Om længder af bars i partitioner
Originalsprog	Engelsk
Tidsskrift	Proceedings of the Edinburgh Mathematical Society
Vol/bind	56
Udgave nummer	2
Sider (fra-til)	535-550
Antal sider	16
ISSN	0013-0915
DOI	https://doi.org/10.1017/s0013091512000387
Status	Udgivet - jun. 2013

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10.1017/s0013091512000387

Citationsformater

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abstract = "We present, given an odd integer d, a decomposition of the multiset of bar lengths of a bar partition λ as the union of two multisets, one consisting of the bar lengths in its d -core partition c d (λ) and the other consisting of modified bar lengths in its d -quotient partition. In particular, we obtain that the multiset of bar lengths in c d (λ) is a sub-multiset of the multiset of bar lengths in λ. Also, we obtain a relative bar formula for the degrees of spin characters of the Schur extensions of n. The proof involves a recent similar result for partitions, proved by Bessenrodt and the authors.",

author = "Gramain, {Jean-Baptiste Bernard} and Olsson, {J{\o}rn B{\o}rling}",

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TY - JOUR

T1 - On bar lengths in partitions

AU - Gramain, Jean-Baptiste Bernard

AU - Olsson, Jørn Børling

PY - 2013/6

Y1 - 2013/6

N2 - We present, given an odd integer d, a decomposition of the multiset of bar lengths of a bar partition λ as the union of two multisets, one consisting of the bar lengths in its d -core partition c d (λ) and the other consisting of modified bar lengths in its d -quotient partition. In particular, we obtain that the multiset of bar lengths in c d (λ) is a sub-multiset of the multiset of bar lengths in λ. Also, we obtain a relative bar formula for the degrees of spin characters of the Schur extensions of n. The proof involves a recent similar result for partitions, proved by Bessenrodt and the authors.

AB - We present, given an odd integer d, a decomposition of the multiset of bar lengths of a bar partition λ as the union of two multisets, one consisting of the bar lengths in its d -core partition c d (λ) and the other consisting of modified bar lengths in its d -quotient partition. In particular, we obtain that the multiset of bar lengths in c d (λ) is a sub-multiset of the multiset of bar lengths in λ. Also, we obtain a relative bar formula for the degrees of spin characters of the Schur extensions of n. The proof involves a recent similar result for partitions, proved by Bessenrodt and the authors.

U2 - 10.1017/s0013091512000387

DO - 10.1017/s0013091512000387

M3 - Journal article

SN - 0013-0915

VL - 56

SP - 535

EP - 550

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 2

ER -

On bar lengths in partitions

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