On bar lengths in partitions

On bar lengths in partitions

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 cd(λ) and the other consisting of modified bar lengths in its d-quotient partition. In particular, we obtai...

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Veröffentlicht in:Proceedings of the Edinburgh Mathematical Society 2013-06, Vol.56 (2), p.535-550
Hauptverfasser: Gramain, Jean-Baptiste, Olsson, Jørn B.
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Sprache:eng
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Decomposition
Integer programming
Integers
Mathematical analysis
Partitions
Proving
Symmetry
Theorems
Unions
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Olsson, Jørn B.
description 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 cd(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 cd(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 $\mathfrak{S}_n$. The proof involves a recent similar result for partitions, proved by Bessenrodt and the authors.
doi_str_mv 10.1017/S0013091512000387
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subjects Decomposition
Integer programming
Integers
Mathematical analysis
Partitions
Proving
Symmetry
Theorems
Unions
title On bar lengths in partitions
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