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Counting partitions by genus

By Jean-Bernard Zuber

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.

Information about the video

  • Date of recording 15/11/2023
  • Date of publication 20/11/2023
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4



  • Jean-Bernard Zuber. Counting partitions by genus. I. Genus 0 to 2. arXiv:2303.05875
  • Robert Coquereaux, Jean-Bernard Zuber. Counting partitions by genus: a compendium of results. arXiv:2305.01100

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