In mathematics, a vexillary permutation is a
permutationμ 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.
Lascoux, Alain; Schützenberger, Marcel-Paul (1982), "Polynômes de Schubert", Comptes Rendus de l'Académie des Sciences, Série I, 294 (13): 447–450,
ISSN0249-6291,
MR0660739
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,
Bibcode:
1985LMaPh..10..111L,
doi:
10.1007/BF00398147,
ISSN0377-9017,
MR0815233
Macdonald, I.G. (1991b),
Notes on Schubert polynomials, Publications du Laboratoire de combinatoire et d'informatique mathématique, vol. 6, Laboratoire de combinatoire et d'informatique mathématique (LACIM), Université du Québec a Montréal,
ISBN978-2-89276-086-6