Elsevier

Discrete Mathematics

Volume 123, Issues 1–3, 15 December 1993, Pages 47-63
Discrete Mathematics

The number of degree restricted maps on general surfaces

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Abstract

Let D be a finite set of positive integers with maximum bigger than two and g,n(g,n) be the number on n-edged rooted maps on the orientable (nonorientable) surface of type g whose face degrees (or, dually, vertex degrees) all lie in D. Define m̂g(x)=n⩾0m̂g,nxn, m̃g(x)=n⩾0m̃g,nxn.

We show that g(x) and g(x) are algebraic functions of a certain form. Asymptotic expressions for g,n and g,n are also derived for some special sets D.

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