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COMBINATORICS
2006

On an Identity for the Cycle Indices of Rooted Tree Automorphism Groups

8 years 11 months ago
On an Identity for the Cycle Indices of Rooted Tree Automorphism Groups
This note deals with a formula due to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symmetric group in some way. An elementary proof is provided as well as some immediate corollaries and applications, in particular a new application to the enumeration of k-decomposable trees. A tree is called k-decomposable in this context if it has a spanning forest whose components are all of size k.
Stephan G. Wagner
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Stephan G. Wagner
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