THE NUMBER OF DEGREE-RESTRICTED ROOTED MAPS ON THE SPHERE

Authors
BENDER EA CANFIELD ER
Citation
Ea. Bender et Er. Canfield, THE NUMBER OF DEGREE-RESTRICTED ROOTED MAPS ON THE SPHERE, SIAM journal on discrete mathematics, 7(1), 1994, pp. 9-15
Citations number
7
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on discrete mathematics → ACNP
ISSN journal
08954801
Volume
7
Issue
1
Year of publication
1994
Pages
9 - 15
Database
ISI
SICI code
0895-4801(1994)7:1<9:TNODRM>2.0.ZU;2-F
Abstract
Let D be a set of positive integers. Let m(n) be the number of n edged rooted maps on the sphere all of whose vertex degrees (or, dually, fa ce degrees) lie in D. Using Brown's technique, the generating function for m(n) implicitly is obtained. It is used to prove that, when gcd ( D) is even, m(n) similar to C(D)n(-5/2)gamma(D)(n). It also yields kno wn-formulas for various special D.