On core and bar-core partitions

Abstract

If $s$ and $t$ are relatively prime J. Olsson proved in 2008 that the $s$-core of a $t$-core partition is again a $t$-core partition, and that the $s$-bar-core of a $t$-bar-core partition is again a $t$-bar-core partition. Here generalized results are proved for partitions and bar-partitions when the restriction that $s$ and $t$ be relatively prime is removed.

References in corpus (2)

• The t-core of an s-core
• The GBG-Rank and t-Cores I. Counting and 4-Cores