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 0196-8858Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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|
|Depositing user:||Pure Administrator|
|Date Deposited:||25 Oct 2011 12:17|
|Last modified:||06 Jan 2017 10:10|