The t-core of an s-core

Abstract

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.

References in corpus (1)

• Containment in (s,t)-core Partitions

Cited by in corpus (9)

• Simultaneous core partitions: parameterizations and sums
• Armstrong's Conjecture for $(k,mk+1)$-Core Partitions
• Strange Expectations
• Symmetry in maximal $(s-1,s+1)$ cores
• $(s,t)$-cores: a weighted version of Armstrong's conjecture
• The $(s,s+d,\dots ,s+pd)$-core partitions and the rational Motzkin paths
• On core and bar-core partitions
• A generalisation of core partitions
• Self-conjugate $(s,s+d,\dots ,s+pd)$-core partitions and free rational Motzkin paths