## The number of partitions of a fixed genus

- Feb. 14, 2020
- 2:30 p.m.

## Abstract

We show that, for any fixed genus g, the ordinary generating function for the genus g partitions of an n-element set into k blocks is algebraic. The proof involves showing that each such partition may be reduced in a unique way to a primitive partition and that the number of primitive partitions of a given genus (regardless of n) is finite. We illustrate our method by finding the generating function for genus 2 partitions, after identifying all genus 2 primitive partitions, using a computer-assisted search. This is joint work with Robert Cori.