Enumeration of non-oriented dessins d'enfants
Organizers
Speaker
Maxim Karev
Time
Thursday, February 26, 2026 1:00 PM - 3:00 PM
Venue
A3-4-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
A classical Grothendieck dessin d'enfant is a proprely vertex-bicolored graph embedded in an oriented surface such that its complement is a union of disks. Equivalently, a dessin can be described by a triple of permutations $(\sigma, \alpha, \phi)$ in the symmetric group $S_n$ satisfying $\sigma \alpha \phi = \mathrm{id}$ and a transitivity condition. Consequently, the enumeration of dessins d'enfants is equivalent to computing structure constants in the group algebra of $S_n$.
In this talk, I will introduce the notion of a non-oriented dessin d'enfant, where the underlying surface is not required to be oriented. I will present an efficient recursion for counting such objects and identify the algebra whose structure constants encode their enumeration. Time permitting, I will also discuss an interpolation between the oriented and non-oriented cases.
In this talk, I will introduce the notion of a non-oriented dessin d'enfant, where the underlying surface is not required to be oriented. I will present an efficient recursion for counting such objects and identify the algebra whose structure constants encode their enumeration. Time permitting, I will also discuss an interpolation between the oriented and non-oriented cases.