The number of degree restricted maps on general surfaces

✍ Scribed by Zhicheng Gao

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 727 KB
• Volume: 123
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90006-f

✦ Synopsis

Let D be a finite set of positive integers with maximum bigger than two and ti,,.(rii,,.) be the number of n-edged rooted maps on the orientable (nonorientable) surface of type 9 whose face degrees (or, dually, vertex degrees) all lie in D. Define A&)= 1 ~g,&", ll>O cl,(x)= 1 fis,"X".

Il>O

We show that k&(x) and m,(x) are algebraic functions of a certain form. Asymptotic expressions for q,,. and %,, are also derived for some special sets D.