Graphical Enumeration: A Species-Theoretic Approach
Combinatorics
2009-09-25 v1
Abstract
An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and used to extend inner plethysm and other operations to virtual species. Finally, inner plethysm and other operations on species are applied to various problems in graph theory. In particular, regular graphs, and digraphs in which every vertex has outdegree k, are enumerated.
Cite
@article{arxiv.math/9811127,
title = {Graphical Enumeration: A Species-Theoretic Approach},
author = {Leopold Travis},
journal= {arXiv preprint arXiv:math/9811127},
year = {2009}
}
Comments
45 pages, 6 figures