Topological enumeration of complex polynomial vector fields

The enumeration of combinatorial classes of the complex polynomial vector fields in $ \mathbb{C} $ presented by K. Dias [Enumerating combinatorial classes of the complex polynomial vector fields in $ \mathbb{C} $. Ergod. Th. & Dynam. Sys. 33 (2013), 416–440] is extended here to a closed form enu...

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Published inErgodic theory and dynamical systems Vol. 35; no. 4; pp. 1315 - 1344
Main Author TOMASINI, J.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2015
Subjects
Combinatorial analysis
Dynamical systems
Enumeration
Exact solutions
Fields (mathematics)
Mathematical analysis
Polynomials
Topological manifolds
Unity
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Summary:The enumeration of combinatorial classes of the complex polynomial vector fields in $ \mathbb{C} $ presented by K. Dias [Enumerating combinatorial classes of the complex polynomial vector fields in $ \mathbb{C} $. Ergod. Th. & Dynam. Sys. 33 (2013), 416–440] is extended here to a closed form enumeration of combinatorial classes for degree $d$ polynomial vector fields up to rotations of the $2(d- 1)\mathrm{th} $ roots of unity. The main tool in the proof of this result is based on a general method of enumeration developed by V. A. Liskovets [Reductive enumeration under mutually orthogonal group actions. Acta Appl. Math. 52 (1998), 91–120].
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ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2013.100