The area above the Dyck path of a permutation

Details The area above the Dyck path of a permutation The area above the Dyck path of a permutation

2008-10-14

arxiv.org/abs/0810.2457v3

Mathematics

Combinatorics

9 pages

Scientific paper

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.

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