In mathematics, a vexillary permutation is a
permutation
In mathematics, a permutation of a set can mean one of two different things:
* an arrangement of its members in a sequence or linear order, or
* the act or process of changing the linear order of an ordered set.
An example of the first mean ...
''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
Module, modular and modularity may refer to the concept of modularity. They may also refer to:
Computer science and engineering
* Modular design, the engineering discipline of designing complex devices using separately designed sub-components
...
.
showed that vexillary
involutions are enumerated by
Motzkin number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have ...
s.
See also
*
Riffle shuffle permutation In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of n items that can be obtained by a single riffle shuffle, in which a sorted deck of n cards is cut into ...
, a subclass of the vexillary permutations
References
*
*
*
*{{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