The t-core of an s-core

Details The t-core of an s-core The t-core of an s-core

2010-07-07

arxiv.org/abs/1007.1071v2

J. Combin. Theory Ser. A 118 (2011) 1525-1539

Mathematics

Combinatorics

Scientific paper

10.1016/j.jcta.2011.01.004

We consider the $t$-core of an $s$-core partition, when $s$ and $t$ are coprime positive integers. Olsson has shown that the $t$-core of an $s$-core is again an $s$-core, and we examine certain actions of the affine symmetric group on $s$-cores which preserve the $t$-core of an $s$-core. Along the way, we give a new proof of Olsson's result. We also give a new proof of a result of Vandehey, showing that there is a simultaneous $s$- and $t$-core which contains all others.

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