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Arithmetical Semigroups Related to Trees and Polyhedra, II — Maps on Surfaces
Author(s) -
Knopfmacher John,
Warlimont Richard
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200202)235:1<59::aid-mana59>3.0.co;2-0
Subject(s) - polyhedron , arithmetic function , mathematics , enumeration , combinatorics , prime (order theory) , discrete mathematics
This paper extends recent investigations by Arnold Knopfmacher and John Knopfmacher [10] of asymptotic enumeration questions concerning finite graphs, trees and polyhedra. The present emphasis is on the counting of non‐isomorphic maps of not necessarily connected finite graphs on arbitrary surfaces. A significant aid towards this goal is provided by an extended abstract prime number theorem, based partly on more delicate tools of analysis due to W. K. Hayman [8].