The area above the Dyck path of a permutation

Mark Dukes, Astrid Reifegerste

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)15-23
Number of pages9
JournalAdvances in Applied Mathematics
Issue number1
Publication statusPublished - Jul 2010


  • permutation
  • Dyck path
  • Simion–Schmidt
  • Bruhat poset


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