The number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves
Kharlamov, Viatcheslav ; Orevkov, S. Yu.
HAL, hal-00013007 / Harvested from HAL
Text on HAL
The 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.
Publié le : 2004-07-05
Classification:  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] 
@article{hal-00013007,
     author = {Kharlamov, Viatcheslav and Orevkov, S. Yu.},
     title = {The number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00013007}
}

Kharlamov, Viatcheslav; Orevkov, S. Yu. The number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00013007/