The $k$-Plancherel measure and a Finite Markov Chain

Svante Linusson, Alperen Özdemir

Let ${\mathcal{P}}_k(n)$ denote the set of partitions of $n$ whose largest part is bounded by $k,$ which are in well-known bijection with $(k+1)$-cores ${\mathcal{C}}_k$. We study a gr…