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

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dc.creatorKharlamov, V.
dc.creatorOrevkov, S.
dc.date2003-01-22
dc.date.accessioned2026-07-07T04:54:37Z
dc.date.available2026-07-07T04:54:37Z
dc.descriptionThe number of topologically different plane real algebraic curves of a given degree $d$ has the form $\exp(C d^2 + o(d^2))$. We determine the best available upper bound for the constant $C$. This bound follows from Arnold inequalities on the number of empty ovals. To evaluate its rate we show its equivalence with the rate of growth of the number of trees half of whose vertices are leaves and evaluate the latter rate.
dc.description13 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0301245
dc.identifierhttp://arxiv.org/abs/math/0301245
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66321
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject14P25; 14H50; 05C05; 05A16
dc.titleThe number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves
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