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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:105

Article

Kharlamov, VM ; Orevkov, SY

关键词: plane real algebraic curve;    ovals arrangement;    unlabeled rooted tree;    asymptotic enumeration;    leaf;    bi-variant generating function;    logarithmic convexity;   

DOI  :  10.1016/j.jcta.2003.10.007

来源: Elsevier

【 摘 要 】

The number of topologically different plane real algebraic curves of a given degree d has the form exp(Cd-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. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free