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)335-350
Number of pages16
JournalProceedings of the Edinburgh Mathematical Society
Issue number2
Early online date21 Mar 2013
Publication statusPublished - Jun 2013


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


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