Selected Article

Title

Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size

Creator

Louchard, Guy

Description

Using the Saddle point method and multiseries expansions, we obtain from the exponential formula and Cauchy's integral formula,asymptotic results for the number $T(n,m,k)$ of partitions of $n$ labeled objects with $m$ blocks of fixed size $k$. We analyze the central and non-central region. In the region $m=n/k-n^\al,\quad 1>\al>1/2$, we analyze the dependence of $T(n,m,k)$ on $\al$. This paper fits within the framework of Analytic Combinatorics.