By Hadrien Notarantonio
By Mireille Bousquet-Mélou
By Igor Kortchemski
By Jérémie Bouttier
Appears in collection : Combinatorics and Arithmetic for Physics: special days 2023
The counting of set partitions according to their genus is revisited. The case of genus 0 – non-crossing partitions – is well known. I will show how, using a functional equation between generating functions, all partitions may be reconstructed from the “(semi)-primitive” ones introduced by Cori and Hetyei. This will be carried out explicitly in genus 1 and 2. Time permitting, known results and conjectures about higher genus will be reviewed.