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no. 4
Twisted Hurwitz numbers: Tropical and polynomial structures
Hahn, Marvin Anas1; Markwig, Hannah2
1 Trinity College Dublin School of Mathematics 17 Westland Row Dublin Ireland
2 Eberhard-Karls-University Tuebingen Fachbereich Mathematik Auf der Morgenstelle 10 72076 Tübingen Germany
Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1075-1101.

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.

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DOI: 10.5802/alco.368
Classification: 14T15, 14N10, 57M12, 05C30
Keywords: Tropical geometry, Hurwitz numbers

Hahn, Marvin Anas 1; Markwig, Hannah 2

1 Trinity College Dublin School of Mathematics 17 Westland Row Dublin Ireland
2 Eberhard-Karls-University Tuebingen Fachbereich Mathematik Auf der Morgenstelle 10 72076 Tübingen Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Hahn, Marvin Anas; Markwig, Hannah. Twisted Hurwitz numbers: Tropical and polynomial structures. Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1075-1101. doi : 10.5802/alco.368. https://alco.centre-mersenne.org/articles/10.5802/alco.368/

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