| Autor: |
Ercolani, Nicholas, Lega, Joceline, Tippings, Brandon |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Nonlinearity 36, 1663-1698 (2023) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1088/1361-6544/acb47d |
| Popis: |
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two asymptotic expansions obtained from two different fields of mathematics: the Riemann-Hilbert analysis of orthogonal polynomials and the theory of discrete dynamical systems. By equating the coefficients of these expansions in a common region of uniform validity in their parameters, we recover known results and provide new expressions for generating functions associated with graphical enumeration on surfaces of genera 0 through 7. Although the body of the article focuses on 4-valent maps, the methodology presented here extends to regular maps of arbitrary even valence and to some cases of odd valence, as detailed in the appendices. |
| Databáze: |
arXiv |
| Externí odkaz: |
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