Partitions, pairs of trees and Catalan numbers
Combinatorics
2010-06-30 v1
Abstract
In "Square partitions and Catalan numbers" (arXiv0912.4983), Bennett et al. presented a recursive algorithm to create a family of partitions from one or several partitions. They were mainly interested in the cases when we begin with a single square partition or with several partitions with only one part. The cardinalities of those families of partitions are the Catalan and ballot numbers, respectively. In this paper we present a closed description for those families. We also present bijections between those sets of partitions and sets of trees and forests enumerated by the Catalan an ballot numbers.
Cite
@article{arxiv.1006.5706,
title = {Partitions, pairs of trees and Catalan numbers},
author = {Eliana Zoque},
journal= {arXiv preprint arXiv:1006.5706},
year = {2010}
}
Comments
13 pages. This paper follows the work done in arXiv0912.4983