Cocktail of partitions

Abstract

A partition of $n$ is a non-increasing sequence of positive integers with sum $n$. This notion namely arises with the representation theory of the symmetric group. To study these representations over a field of characteristic $p$ one can use the $p$-regularisation process, introduced by James, which to a partition associates a $p$-regular partition, that is, a partition with no part repeating $p$ times or more. A classical measure on the set of partitions of $n$ is the Plancherel measure. A spectacular result of Kerov–Vershik and Logan–Shepp (1977) gives an asymptotic limit shape for large partitions under the Plancherel measure. In this talk, we will show what this result gives for the $p$-regularisations of large partitions. Namely, there is still a limit shape, given by the shaking of the Kerov-Vershik-Logan-Shepp curve.

Date
Location
IDP (Tours)