Abstract
Calculations of genus polynomials are given for three kinds of dipoles: with no loops; with a loop at one vertex; or with a loop at both vertices. We include a very concise, elementary derivation of the genus polynomial of a loopless dipole. To describe the general effect on the face-count and genus polynomials of the operation of adding a loop at a vertex, we introduce imbedding types that are partitions of integers, specifically, partitions of the valences of the vertices at which loops are to be added. Adding a loop at a root-vertex changes the possible number of imbedding types from the number of partitions of the valence prior to adding the loop to the number of partitions of the valence afterward.
Original language | American English |
---|---|
Pages (from-to) | 203-221 |
Number of pages | 19 |
Journal | Australasian Journal of Combinatorics |
Volume | 67 |
Issue number | 2 |
State | Published - 2017 |
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics