Algebra and Combinatorics Research Group

Seminar: Spring 2008, Fridays, Milner 317, 3:00–3:50 p.m.


March 21

Rosena Du ( East China Normal University )


Counting Labelled Trees with Given Indegree Sequence

Abstract: For a labelled tree on the vertex set $[n]:=\{1,2,\ldots, n\}$, define the direction of each edge $ij$ to be $i\rightarrow j$ if $i < j$. The indegree sequence of $T$ can be considered as a partition $\lambda \vdash n-1$. The enumeration of trees with a given indegree sequence arises in counting secant planes of curves in projective spaces. Recently Ethan Cotterill conjectured a formula for the number of trees on $[n]$ with indegree sequence corresponding to a partition $\lambda$. In this talk I will give two proofs of Cotterill's conjecture: one is "semi-combinatorial" based on induction, the other is a bijective proof. (This is joint work with Jingbin Yin.)

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