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The area above the Dyck path of a permutation
- Source :
-
Advances in Applied Mathematics . Jul2010, Vol. 45 Issue 1, p15-23. 9p. - Publication Year :
- 2010
-
Abstract
- 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01968858
- Volume :
- 45
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 50225881
- Full Text :
- https://doi.org/10.1016/j.aam.2009.11.008