منابع مشابه
Counting rooted maps on a surface
Several enumeration results are known about rooted maps on orientable surfaces, whereas rooted maps on non-orientable surfaces have seldom been studied. First, we unify both kind of maps, giving general functional equations for the generating series which counts rooted maps on any locally orientable surface, by number of vertices and faces. Then, we formally solve these equations, in order to e...
متن کاملCounting Rooted Trees
Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for the class of rooted trees: C · ρ−n · n−3/...
متن کاملCounting Rooted Trees 3
Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for the class of rooted trees: C · ρ−n · n−3/...
متن کاملEfficient enumeration of rooted maps of a given orientable genus by number of faces and vertices
We simplify the recurrence satisfied by the polynomial part of the generating function that counts rooted maps of positive orientable genus g by number of vertices and faces. We have written an optimized program in C++ for computing this generating function and constructing tables of numbers of rooted maps, and we describe some of these optimizations here. Using this program we extended the enu...
متن کاملCharacter Theory and Rooted Maps in an Orientable Surface of given Genus: Face-colored Maps
The character theoretic approach [5] to the enumeration of rooted maps in an orientable surface of arbitrary genus is extended to 2-face-colorable rooted maps. In particular, we show that there exists, for each genus, a correspondence between the set of 2-colored triangulations and a set of 2-colored rooted maps of all lower genera with a distinguished subset of vertices.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1972
ISSN: 0095-8956
DOI: 10.1016/0095-8956(72)90049-4