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arXiv · 0810.2457

The area above the Dyck path of a permutation

Mark Dukes·Astrid Reifegerste
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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 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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Mark Dukes, Astrid Reifegerste. 2009-11-25. The area above the Dyck path of a permutation. https://arxiv.org/abs/0810.2457

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