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- W3180894320 abstract "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 $lambda$ is at most the $p$-bar-weight of $lambda$. 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 $tilde C_{tfrac{(p-1)}{2}}timestilde C_{tfrac{(q-1)}{2}}$. We also provide an algorithm for constucting a bar partition in this set with a given $p$-bar-core and $q$-bar-core." @default.
- W3180894320 created "2021-07-19" @default.
- W3180894320 creator A5047498064 @default.
- W3180894320 date "2021-07-09" @default.
- W3180894320 modified "2023-09-27" @default.
- W3180894320 title "A further generalisation of bar-core partitions." @default.
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