Genus distributions for bouquets of circles

The genus distribution of a graph G is defined to be the sequence { g m } such that g m is the number of different imbeddings of G in the closed orientable surface of genus m. A counting formula of D. M. Jackson concerning the cycle structure of permutations is used to derive the genus distribution...

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Bibliographic Details
Published inJournal of combinatorial theory. Series B Vol. 47; no. 3; pp. 292 - 306
Main Authors Gross, Jonathan L, Robbins, David P, Tucker, Thomas W
Format Journal Article
LanguageEnglish
Published Duluth, MN Elsevier Inc 01.12.1989
Academic Press
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Arc
Permutation
Topological graph
Genus
Distribution
Graph theory
Emludding
Rotation
Surface
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Summary:The genus distribution of a graph G is defined to be the sequence { g m } such that g m is the number of different imbeddings of G in the closed orientable surface of genus m. A counting formula of D. M. Jackson concerning the cycle structure of permutations is used to derive the genus distribution for any bouquet of circles B n . It is proved that all these genus distributions for bouquets are strongly unimodal.
ISSN:0095-8956
1096-0902
DOI:10.1016/0095-8956(89)90030-0