Bicoloured Ordered Trees, Non-Nesting Partitions and Non-Crossing Partitions

Abstract

Using a new way to label edges in a bicoloured ordered tree,we introduce a bijection between bicoloured ordered trees and non-nesting partitions. Consequently, enumerative results of non-nesting partitions are derived. Together with another bijection given before, we obtain a bijection between non-nesting partitions and non-crossing partitions specified with four parameters.