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.
 showed that vexillary involutions are enumerated by Motzkin numbers.