Asymptotic Enumeration of Constellations and Related Families of Maps on Orientable Surfaces
نویسنده
چکیده
We perform the asymptotic enumeration of two classes of rooted maps on orientable surfaces:m-hypermaps andm-constellations. Form = 2 they correspond respectively to maps with even face degrees and bipartite maps. We obtain explicit asymptotic formulas for the number of such maps with any finite set of allowed face degrees. Our proofs combine a bijective approach, generating series techniques related to lattice walks, and elementary algebraic graph theory. A special case of our results implies former conjectures of Z. Gao.
منابع مشابه
Counting one-face maps on non-orientable surfaces
A unicellular map is the embedding of a connected graph in a surface, such that the complement of the graph is a topological polygon. In this paper we address the problem of counting unicellular maps according to the number of edges and the Euler characteristic of the surface. For orientable surfaces, this enumeration problem was popularized by Harer and Zagier who discovered a strikingly simpl...
متن کاملLinfan Mao Automorphism Groups of Maps, Surfaces and Smarandache Geometries
A combinatorial map is a connected topological graph cellularly embeddedin a surface. This monograph concentrates on the automorphism groupof a map, which is related to the automorphism groups of a Klein surfaceand a Smarandache manifold, also applied to the enumeration of unrootedmaps on orientable and non-orientable surfaces. A number of results for theautomorphism groups ...
متن کاملIsomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds
We present a fast enumeration algorithm for combinatorial 2and 3-manifolds. In particular, we enumerate all triangulated surfaces with 11 and 12 vertices and all triangulated 3-manifolds with 11 vertices. We further determine all equivelar maps on the non-orientable surface of genus 4 as well as all equivelar triangulations of the orientable surface of genus 3 and the non-orientable surfaces of...
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 کاملAsymptotic Enumeration of Reversible Maps Regardless of Genus∗
We derive asymptotic expansions for the numbers U(n) of isomorphism classes of sensed maps on orientable surfaces with given number of edges n, where we do not specify the genus and for the numbers A(n) of reflexible maps with n edges. As expected the ratio A(n)/U(n) → 0 for n → ∞. This shows that almost all maps are chiral. Moreover, we show logA(n) ∼ 12 logU(n) ∼ (n/2) log n. Due to a corresp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 18 شماره
صفحات -
تاریخ انتشار 2009