Graphical Enumeration: A Species-Theoretic Approach

Details Graphical Enumeration: A Species-Theoretic Approach Graphical Enumeration: A Species-Theoretic Approach

1998-11-21

arxiv.org/abs/math/9811127v1

Mathematics

Combinatorics

45 pages, 6 figures

Scientific paper

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.

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