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

Official URL: http://dx.doi.org/10.1016/j.aam.2009.11.008

## 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.

Item type: | Article |
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ID code: | 34499 |

Keywords: | permutation, Dyck path, Simion–Schmidt, Bruhat poset, Electronic computers. Computer science, Applied Mathematics |

Subjects: | Science > Mathematics > Electronic computers. Computer science |

Department: | Faculty of Science > Computer and Information Sciences |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 25 Oct 2011 13:17 |

Last modified: | 05 Sep 2014 12:02 |

URI: | http://strathprints.strath.ac.uk/id/eprint/34499 |

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