Proof of Two Combinatorial Results Arising in Algebraic Geometry

Abstract

For a labeled tree on the vertex set [n] := {1, 2, . . . , n}, define the direction of each edge ij as i → j if i < j. The indegree sequence λ = 1122 . . . is then a partition of n−1. Let aλ be the number of trees on [n] with indegree sequence λ. In a recent paper (arXiv:0706.2049v2) Cotterill stumbled across the following two remarkable formulas aλ = (n− 1)! (n− k)!e1!(1!)1e2!(2!)2 . . . and

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Cite this paper

@inproceedings{Shin2008ProofOT, title={Proof of Two Combinatorial Results Arising in Algebraic Geometry}, author={Heesung Shin and Jiang Zeng}, year={2008} }