Geodesic
\(\Gamma \)-species and the enumeration of \(k\)-trees
Andrew Gainer-Dewar1
1Carleton College
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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We study the class of graphs known as $k$-trees through the lens of Joyal’s theory of combinatorial species (and a extension known as 'Γ-species' which incorporates data about 'structural' group actions). This culminates in a system of recursive functional equations giving the generating function for unlabeled $k$-trees which allows for fast, efficient computation of their numbers. Enumerations up to $k = 10$ and $n = 30$ (for a k-tree with $n + k − 1$ vertices) are included in tables, and Sage code for the general computation is included in an appendix.
DOI : 10.37236/2615
Classification : 05C30, 05E18
Mots-clés : combinatorial species, \(k\)-trees

Andrew Gainer-Dewar  1

1 Carleton College 
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Andrew Gainer-Dewar. \(\Gamma \)-species and the enumeration of \(k\)-trees. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2615

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