Year: 2024
Type: article
Abstract: Hurwitz numbers count covers of curves satisfying fixed ramification data. Via monodromy representation, this counting problem can be transformed to a problem of counting factorizations in the symmetric group. This and other beautiful connections make Hurwitz numbers a longstanding active research topic. In recent work [4], a new enumerative invariant called b -Hurwitz number was introduced, which enumerates non-orientable branched coverings. For b = 1 , we obtain twisted Hurwitz numbers which were linked to surgery theory in [1] and admit a representation as factorisations in the symmetric group. In this paper, we derive a tropical interpretation of twisted Hurwitz numbers in terms of tropical covers and study their polynomial structure.
Source: Algebraic Combinatorics
DOI: 10.5802/alco.368
Authors: Marvin Anas Hahn, Hannah Markwig
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4402191336