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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Vydané v:Ergodic theory and dynamical systems Ročník 35; číslo 4; s. 1315 - 1344
Hlavný autor: TOMASINI, J.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cambridge, UK Cambridge University Press 01.06.2015
Predmet:
Combinatorial analysis
Dynamical systems
Enumeration
Exact solutions
Fields (mathematics)
Mathematical analysis
Polynomials
Topological manifolds
Unity
ISSN:0143-3857, 1469-4417
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Shrnutí: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