2008/10/14 by Dukes, Mark, Reifegerste, Astrid
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.0810.2457
In this paper we study a mapping from permutations to Dyck paths. A Dyck path gives rise to a (Young) diagram and we give relationships between statistics on permutations and statistics on their corresponding diagrams. The distribution of the size of this diagram is discussed and a generalisation given of a parity result due to Simion and Schmidt. We propose a filling of the diagram which determines the permutation uniquely. Diagram containment on a restricted class of permutations is shown to be related to the strong Bruhat poset.