The t-core of an s-core
Copyright policy )The t-core of an s-core
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.
- Queen Mary University of London United Kingdom
- University of London United Kingdom
- UNIVERSITY OF LONDON United Kingdom
Combinatorial aspects of partitions of integers, Affine symmetric group, core, Representations of finite symmetric groups, partition, rim hook, Theoretical Computer Science, affine symmetric group, Computational Theory and Mathematics, Combinatorial aspects of representation theory, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Core, Young diagram, Combinatorics (math.CO), Partition
Combinatorial aspects of partitions of integers, Affine symmetric group, core, Representations of finite symmetric groups, partition, rim hook, Theoretical Computer Science, affine symmetric group, Computational Theory and Mathematics, Combinatorial aspects of representation theory, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Core, Young diagram, Combinatorics (math.CO), Partition
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