Projects per year
Abstract
Harer and Zagier proved a recursion to enumerate gluings of a 2dgon that result in an orientable genus g surface, in their work on Euler characteristics of moduli spaces of curves. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: how large is the family of problems for which these socalled 1point recursions exist? In this paper, we prove the existence of 1point recursions for a class of enumerative problems that have Schur function expansions. In particular, we recover the Harer–Zagier recursion, but our methodology also applies to the enumeration of dessins d’enfant, to BousquetMélou–Schaeffer numbers, to monotone Hurwitz numbers, and more. On the other hand, we prove that there is no 1point recursion that governs single Hurwitz numbers. Our results are effective in the sense that one can explicitly compute particular instances of 1point recursions, and we provide several examples. We conclude the paper with a brief discussion and a conjecture relating 1point recursions to the theory of topological recursion.
Original language  English 

Pages (fromto)  469503 
Number of pages  35 
Journal  Journal of Algebraic Combinatorics 
Volume  53 
Issue number  2 
DOIs  
Publication status  Published  Mar 2021 
Keywords
 1point functions
 Dessins d’enfant
 Harer–Zagier formula
 Holonomic functions
 Hurwitz numbers
 Ribbon graphs
 Schur functions
Projects
 2 Finished

Frobenius manifolds from a geometrical and categorical viewpoint
Norbury, P. T., Murfet, D. & Do, N.
2/03/18 → 31/12/20
Project: Research

The geometry and combinatorics of moluli spaces
Australian Research Council (ARC)
30/06/13 → 30/08/18
Project: Research