2007/12/24 by Rosena R. X. Du, Du, Rosena R. X., Jingbin Yin +1 · 1 citation
Computer Science · Mathematics · #05A15 #05A18 #05C07 #Advanced Combinatorial Mathematics #Advanced Database Systems and Queries #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #math.CO #msc:05A15 #msc:05A18 #msc:05C07
paper · pdf · doi:10.48550/arxiv.0712.4032
10 pages
openalex publication_date 2007/12/24 · arxiv created 2009/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a labelled tree on the vertex set [n]:=\1,2,..., n\, define the direction of each edge ij to be i→ j if i<j. The indegree sequence of T can be considered as a partition λ\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 λ. In this paper we give two proofs of Cotterill's conjecture: one is `semi-combinatorial" based on induction, the other is a bijective proof.