Valence-partitioned genus polynomials and their application to generalized dipoles

Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)203-221
Number of pages19
JournalAustralasian Journal of Combinatorics
Volume67
Issue number2
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Fingerprint

Dive into the research topics of 'Valence-partitioned genus polynomials and their application to generalized dipoles'. Together they form a unique fingerprint.

Cite this