Combinatorics of Bousquet-M\'elou-Schaeffer numbers in the light of topological recursion
2019
In this paper we prove, in a purely combinatorial way, a structural quasi-polynomiality property for the Bousquet-Melou-Schaeffer numbers. Conjecturally, this property should follow from the Chekhov-Eynard-Orantin topological recursion for these numbers (or, to be more precise, the Bouchard-Eynard version of the topological recursion for higher order critical points), which we derive in this paper from the recent result of Alexandrov-Chapuy-Eynard-Harnad. To this end, the missing ingredient is a generalization to the case of higher order critical points on the underlying spectral curve of the existing correspondence between the topological recursion and Givental's theory for cohomological field theories.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
44
References
0
Citations
NaN
KQI