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Topological enumeration of complex polynomial vector fields

Published online by Cambridge University Press:  10 January 2014

J. TOMASINI
J. TOMASINI*
Affiliation:
Laboratoire Angevin de REcherche en MAthématiques (LAREMA), Université d’Angers, France email [email protected]
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Abstract

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].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 4 , June 2015 , pp. 1315 - 1344
Copyright
© Cambridge University Press, 2014 

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