On the lower bounds for real double Hurwitz numbers

As the real counterpart of double Hurwitz number, the real double Hurwitz number depends on the distribution of real branch points. We consider the problem of asymptotic growth of real and complex double Hurwitz numbers. We provide a lower bound for real double Hurwitz numbers based on the tropical...

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2023-03, Vol.57 (2), p.525-546
Main Author: Ding, Yanqiao
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Lower bounds
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
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Summary:As the real counterpart of double Hurwitz number, the real double Hurwitz number depends on the distribution of real branch points. We consider the problem of asymptotic growth of real and complex double Hurwitz numbers. We provide a lower bound for real double Hurwitz numbers based on the tropical computation of real double Hurwitz numbers. By using this lower bound and J. Rau’s result ( Math Ann 375: 895-915, 2019), we prove the logarithmic equivalence of real and complex Hurwitz numbers.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-022-01213-3