Projects per year
Abstract
Given a surface with boundary and some points on the boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on the surface. If only bigons are allowed, then one obtains the notion of arc diagrams, whose enumeration is known to have a rich structure. We show that the count of polygon diagrams on surfaces with any genus and number of boundary components exhibits similar structure. In particular it is almost polynomial in the number of points on the boundary components, and the leading coefficients of those polynomials are intersection numbers on compactified moduli spaces of curves.
Original language | English |
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Article number | P4.9 |
Number of pages | 47 |
Journal | The Electronic Journal of Combinatorics |
Volume | 28 |
Issue number | 4 |
DOIs | |
Publication status | Published - 22 Oct 2021 |
Projects
- 2 Finished
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Frobenius manifolds from a geometrical and categorical viewpoint
Norbury, P. T. (Primary Chief Investigator (PCI)), Murfet, D. (Chief Investigator (CI)) & Do, N. (Chief Investigator (CI))
2/03/18 → 31/12/20
Project: Research
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Quantum invariants and hyperbolic manifolds in three-dimensional topology
Australian Research Council (ARC), Monash University
1/01/16 → 31/07/20
Project: Research