On the Convergence of Monotone Hurwitz Generating Functions
| Autor: | Ian P. Goulden, Jonathan Novak, Mathieu Guay-Paquet |
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| Rok vydání: | 2017 |
| Předmět: |
Mathematics::Number Theory
010102 general mathematics Mathematics::Classical Analysis and ODEs Algebraic geometry 01 natural sciences Upper and lower bounds Structural theory Combinatorics chemistry.chemical_compound Mathematics::Algebraic Geometry Monotone polygon chemistry Genus (mathematics) 0103 physical sciences Convergence (routing) FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Annals of Combinatorics. 21:73-81 |
| ISSN: | 0219-3094 0218-0006 |
| DOI: | 10.1007/s00026-017-0341-5 |
| Popis: | Monotone Hurwitz numbers were introduced by the authors as a combinatorially natural desymmetrization of the Hurwitz numbers studied in enumerative algebraic geometry. Over the course of several papers, we developed the structural theory of monotone Hurwitz numbers and demonstrated that it is in many ways parallel to that of their classical counterparts. In this note, we identify an important difference between the monotone and classical worlds: fixed-genus generating functions for monotone double Hurwitz numbers are absolutely summable, whereas those for classical double Hurwitz numbers are not. This property is crucial for applications of monotone Hurwitz theory in analysis. We quantify the growth rate of monotone Hurwitz numbers in fixed genus by giving universal upper and lower bounds on the radii of convergence of their generating functions. 8 pages, 1 figure |
| Databáze: | OpenAIRE |
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