Klazar trees and perfect matchings
| dc.creator | Callan, David | |
| dc.date | 2008-10-27 | |
| dc.date.accessioned | 2026-07-07T10:13:28Z | |
| dc.date.available | 2026-07-07T10:13:28Z | |
| dc.description | Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps most interesting of these weights, w_{12}, led to a recurrence relation and an identity for which he requested combinatorial explanations. Here we provide such explanations. To do so, we introduce the notion of a "Klazar violator" vertex in an increasing ordered tree and observe that w_{12} counts what we call Klazar trees--increasing ordered trees with no Klazar violators. A highlight of the paper is a bijection from n-edge increasing ordered trees to perfect matchings of [2n]={1,2,...,2n} that sends Klazar violators to even numbers matched to a larger odd number. We find the distribution of the latter matches and, in particular, establish the one-summation explicit formula sum_{k=1}^{lfloor n/2 rfloor}(2k-1)!!^2 StirlingPartition{n+1}{2k+1} for the number of perfect matchings of [2n] with no even-to-larger-odd matches. The proofs are mostly bijective. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0810.4901 | |
| dc.identifier | http://arxiv.org/abs/0810.4901 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172538 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | Klazar trees and perfect matchings | |
| dc.type | text |