Orateur
Prof.
Jean-Bernard Zuber
(LPTHE, Sorbonne Université)
Description
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 (based on arxiv:2303.05875 and 2305.01100).
