Partitions, pairs of trees and Catalan numbers

Details Partitions, pairs of trees and Catalan numbers Partitions, pairs of trees and Catalan numbers

2010-06-29

arxiv.org/abs/1006.5706v1

Mathematics

Combinatorics

13 pages. This paper follows the work done in arXiv0912.4983

Scientific paper

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.

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