17 citations · 17 across the 5 of their papers we have counts for
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Pólya theory for species with an equivariant group action
Andrew Gainer-Dewar
Joyal's theory of combiantorial species provides a rich and elegant framework for enumerating combinatorial structures by translating structural information into algebraic function…
Enumeration of labeled and unlabeled k-gonal and polygonal 2-trees and succulents by vertices
Andrew Gainer-Dewar
We use the theory of Γ-species to enumerate k-gonal and polygonal 2-trees with respect to their vertices. We then extend this result to enumerate "succulents", a tree-like class of…
Counting unlabeled k-trees
Andrew Gainer-Dewar, Ira M. Gessel
We count unlabeled k-trees by properly coloring them in k+1 colors and then counting orbits of these colorings under the action of the symmetric group on the colors.
Enumeration of bipartite graphs and bipartite blocks
Andrew Gainer-Dewar, Ira M. Gessel
Using the theory of combinatorial species, we compute the cycle index for bipartite graphs, which we use to count unlabeled bipartite graphs and bipartite blocks.
Γ-species and the enumeration of k-trees
Andrew Gainer-Dewar
We study the class of graphs known as k-trees through the lens of Joyal's theory of combinatorial species (and an equivariant extension known as '-species' which incorporates da…