Vexillary permutation

Short description: Type of permutation

In mathematics, a vexillary permutation is a permutation μ of the positive integers containing no subpermutation isomorphic to the permutation (2143); in other words, there do not exist four numbers i < j < k < l with μ(j) < μ(i) < μ(l) < μ(k). They were introduced by Lascoux and Schützenberger (1982, 1985). The word "vexillary" means flag-like, and comes from the fact that vexillary permutations are related to flags of modules.

(Guibert Pergola) showed that vexillary involutions are enumerated by Motzkin numbers.

## See also

* Riffle shuffle permutation, a subclass of the vexillary permutations

## References

* Guibert, O.; Pergola, E.; Pinzani, R. (2001), "Vexillary involutions are enumerated by Motzkin numbers", Annals of Combinatorics 5 (2): 153–174, doi:10.1007/PL00001297, ISSN 0218-0006
* Lascoux, Alain; Schützenberger, Marcel-Paul (1982), "Polynômes de Schubert", Comptes Rendus de l'Académie des Sciences, Série I 294 (13): 447–450, ISSN 0249-6291
* Lascoux, Alain; Schützenberger, Marcel-Paul (1985), "Schubert polynomials and the Littlewood–Richardson rule", Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics 10 (2): 111–124, doi:10.1007/BF00398147, ISSN 0377-9017, Bibcode: 1985LMaPh..10..111L
* Macdonald, I.G. (1991b), Notes on Schubert polynomials, Publications du Laboratoire de combinatoire et d'informatique mathématique, 6, Laboratoire de combinatoire et d'informatique mathématique (LACIM), Université du Québec a Montréal, ISBN 978-2-89276-086-6, https://books.google.com/books?id=BvLuAAAAMAAJ

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