A generalisation of bar-core partitions
Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 667-698.

When p and q are coprime odd integers no less than 3, Olsson proved that the q-bar-core of a p-bar-core is again a p-bar-core. We establish a generalisation of this theorem: that the p-bar-weight of the q-bar-core of a bar partition λ is at most the p-bar-weight of λ. We go on to study the set of bar partitions for which equality holds and show that it is a union of orbits for an action of a Coxeter group of type C ˜ (p-1)/2 ×C ˜ (q-1)/2 . We also provide an algorithm for constructing a bar partition in this set with a given p-bar-core and q-bar-core.

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DOI: 10.5802/alco.231
Classification: 05E10,  05A17,  20C30
Keywords: representation theory, symmetric group, partitions, projective, bar-core
Yates, Dean 1

1 Queen Mary, University of London Mile End Road Bethnal Green London E1 4NS
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Yates, Dean. A generalisation of bar-core partitions. Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 667-698. doi : 10.5802/alco.231. https://alco.centre-mersenne.org/articles/10.5802/alco.231/

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