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

Authors:
V. M. Kharlamov;S. Yu. Orevkov
Affiliations:
Université Louis Pasteur et IRMA (CNRS), 7 rue René Descartes Strasbourg Cedex 67084, France;Laboratoire Emile Picard, UFR MIG, Univ. Paul Sabatier, 118 route de Narbonne, Toulouse 31062, France
Venue:
Journal of Combinatorial Theory Series A
Year:
2004

Citing 2
Cited 1

The art of computer programming, volume 1 (3rd ed.): fundamental algorithms

The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The distribution of nodes of given degree in random trees

Journal of Graph Theory

Isotopic triangulation of a real algebraic surface

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

The number of topologically different plane real algebraic curves of a given degree d has the form exp(Cd2 + o(d2)). 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.