### 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 o_{n}. The proof involves a recent similar result for partitions, proved by Bessenrodt and the authors.

Original language | English |
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Pages (from-to) | 335-350 |

Number of pages | 16 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 56 |

Issue number | 2 |

Early online date | 21 Mar 2013 |

DOIs | |

Publication status | Published - Jun 2013 |

### Keywords

- bar lengths
- bar partitions
- covering groups
- partitions
- symmetric group

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Gramain, J. B., & Olsson, J. B. (2013). On bar lengths in partitions.

*Proceedings of the Edinburgh Mathematical Society*,*56*(2), 335-350. https://doi.org/10.1017/S0013091512000387