Submap Density and Asymmetry Results for Two Parameter Map Families

Authors:
Edward A. Bender;E. Rodney Canfield;Zhicheng Gao;L. Bruce Ricmond
Affiliations:
Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA;Department of Computer Science, University of Georgia, Athens, GA 30602, USA;Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Venue:
Combinatorics, Probability and Computing
Year:
1997

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Abstract

Let ℳn,k(S) be the set of n-edge k-vertex rooted maps in some class on the surface S. Let P be a planar map in the class. We develop a method for showing that almost all maps in ℳn,k(S) contain many copies of P. One consequence of this is that almost all maps in ℳn,k(S) have no symmetries. The classes considered include c-connected maps (c ≤ 3) and certain families of degree restricted maps.