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 . The word "vexillary" means flag-like, and comes from the fact that vexillary permutations are related to
flags
A flag is a piece of fabric (most often rectangular) with distinctive colours and design. It is used as a symbol, a signalling device, or for decoration. The term ''flag'' is also used to refer to the graphic design employed, and flags have ...
of
modules.
showed that vexillary
involutions are enumerated by
Motzkin numbers.
See also
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Riffle shuffle permutation, a subclass of the vexillary permutations
References
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*{{Citation , last1=Macdonald , first1=I.G. , author1-link=Ian G. Macdonald , title=Notes on Schubert polynomials , url=https://books.google.com/books?id=BvLuAAAAMAAJ , publisher=Laboratoire de combinatoire et d'informatique mathématique (LACIM), Université du Québec a Montréal , series=Publications du Laboratoire de combinatoire et d'informatique mathématique , isbn=978-2-89276-086-6 , year=1991b , volume=6
Permutation patterns