On bar lengths in partitions

Jean Baptiste Gramain*, Jørn B. Olsson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 on. The proof involves a recent similar result for partitions, proved by Bessenrodt and the authors.

Original languageEnglish
Pages (from-to)535-550
Number of pages16
JournalProceedings of the Edinburgh Mathematical Society
Issue number2
Early online date21 Mar 2013
Publication statusPublished - Jun 2013

Bibliographical note

J.-B.G. gratefully acknowledges financial support from a grant of the Agence Nationale de la Recherche (ANR-10-PDOC-021-01). He also expresses his gratitude to J. B. Olsson and J. Grodal for their (not only financial) support during
his stay at the University of Copenhagen, where most of this work was done. Finally, the authors thank C. Bessenrodt for useful discussions and for a careful reading of the manuscript, thereby pointing out a problem in an earlier version of this work.


  • bar lengths
  • bar partitions
  • covering groups
  • partitions
  • symmetric group


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