论文标题
扭曲的Hurwitz数字：热带和多项式结构
Twisted Hurwitz numbers: Tropical and polynomial structures
论文作者
论文摘要
Hurwitz数字计数曲线涵盖满足固定分支数据的曲线。通过单肌表示，该计数问题可以转化为对称组中计数因素化的问题。这个和其他美丽的联系使Hurwitz数字成为长期活跃的研究主题。在最近的工作Chapuy和Dolęga中，引入了一种名为B-Hurwitz编号的新列举不变的，该数字列举了不可方向的分支覆盖物。对于B = 1，我们获得了扭曲的Hurwitz数字，这些数字与Burman和Fesler的工作中的手术理论有关，并承认表示对称群体中的分解。在本文中，我们从热带覆盖物和研究其多项式结构方面得出了扭曲的Hurwitz数量的热带插入。
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 Chapuy and Dolęga, 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 work of Burman and Fesler and admit a representation as factorisations in the symmetric group. In this paper, we derive a tropical interperetation of twisted Hurwitz numbers in terms of tropical covers and study their polynomial structure.
