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The area above the Dyck path of a permutation

Dukes, Mark and Reifegerste, Astrid (2010) The area above the Dyck path of a permutation. Advances in Applied Mathematics, 45 (1). pp. 15-23. ISSN 0196-8858

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Abstract

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 generalization 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.