Vexillary 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&nbsp;<&nbsp;j&nbsp;<&nbsp;k&nbsp;<&nbsp;l with μ(j)&nbsp;<&nbsp;μ(i)&nbsp;<&nbsp;μ(l)&nbsp;<&nbsp;μ(k). They were introduced by . 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.

See also

• Riffle shuffle permutation, a subclass of the vexillary permutations

References