The number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves.

DOI10.1016/j.jcta.2003.10.007zbMath1053.14064arXivmath/0301245OpenAlexW1970068976MaRDI QIDQ1427013

Viatcheslav Kharlamov, Stepan Yu. Orevkov

Publication date: 14 March 2004

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0301245

zbMATH Keywords

asymptotic enumerationleaflogarithmic convexitybi-variant generating functionovals arrangementunlabled rooted trees

Mathematics Subject Classification ID

Applications of graph theory (05C90) Real algebraic sets (14P05) Enumeration in graph theory (05C30) Plane and space curves (14H50) Enumerative problems (combinatorial problems) in algebraic geometry (14N10)

Related Items (3)

Topology and counting of real algebraic curves ⋮ Maximally writhed real algebraic links ⋮ Isotopic triangulation of a real algebraic surface

Cites Work

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• Distribution of ovals of the real plane of algebraic curves, of involutions of four-dimensional smooth manifolds, and the arithmetic of integer-valued quadratic forms
• The distribution of degrees in a large random tree
• An asymptotic evaluation of the cycle index of a symmetric group
• Asymptotic growth of the number of classes of real plane algebraic curves as the degree grows
• The number of trees
• The distribution of nodes of given degree in random trees

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