A Character Theoretic Approach to Embed Dings of Rooted Maps in an Orientable Surface of given Genus
نویسندگان
چکیده
The group algebra of the symmetric group and properties of the irreducible characters are used to derive combinatorial properties of embeddings of rooted maps in orientable surfaces of arbitrary genus. In particular, we show that there exists, for each genus, a correspondence between the set of rooted quadrangulations and a set of rooted maps of all lower genera with a distinguished subset of vertices.
منابع مشابه
Character 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 کاملCounting 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 کاملA new approach for enumerating maps on orientable surfaces
Classifying embeddings of a given graph G on orientable surfaces under the action of its automorphisms, a relation between the genus distribution of rooted maps and embeddings of graph G on orientable surfaces is established. Applying this relation enables us to enumerate rooted maps by automorphism groups or by enumerating labelled graphs with vertex partition and find new formulas for the num...
متن کاملA Nebeský-Type Characterization for Relative Maximum Genus
This paper concerns the maximum genus orientable surface upon which a given graph cellularly embeds. Classical theorems of Xuong and Nebesk y give exact values for the maximum genus. The former is suited to constructing embeddings while the latter is suited to forbidding embeddings of larger genus. However, using either theorem alone requires an exhaustive search to establish the exact value. H...
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 کامل