Counting Labelled Trees with Given Indegree Sequence
| dc.creator | Du, Rosena R. X. | |
| dc.creator | Yin, Jingbin | |
| dc.date | 2007-12-24 | |
| dc.date | 2009-04-02 | |
| dc.date.accessioned | 2026-07-07T12:58:45Z | |
| dc.date.available | 2026-07-07T12:58:45Z | |
| dc.description | For a labelled tree on the vertex set $[n]:=\{1,2,..., n\}$, define the direction of each edge $ij$ to be $i\to j$ 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. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0712.4032 | |
| dc.identifier | http://arxiv.org/abs/0712.4032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225346 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 05C07, 05A18 | |
| dc.title | Counting Labelled Trees with Given Indegree Sequence | |
| dc.type | text |