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math.GT2003
Plane real algerbaic curves of odd degree with a deep nest
Stepan Yu Orevkov
We apply Murasugi-Tristram inequality to real algebraic curves of odd degree on with a deep nest, i.e. a nest of the depth where is the degree. For such curves,…
math.AG2003
The number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves
V. Kharlamov, S. Orevkov
The number of topologically different plane real algebraic curves of a given degree has the form . We determine the best available upper bound for the con…