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 < j < k < l with μ(j) < μ(i) < μ(l) < μ(k). They were introduced by {{harvs|txt|last1=Lascoux|last2=Schützenberger|year1=1982|year2=1985}}. The word "vexillary" means flag-like, and comes from the fact that vexillary permutations are related to flags of modules.
{{harvtxt|Guibert|Pergola|Pinzani|2001}} showed that vexillary involutions are enumerated by Motzkin numbers.
See also
- Riffle shuffle permutation, a subclass of the vexillary permutations
References
- {{Citation | last1=Guibert | first1=O. | last2=Pergola | first2=E. | last3=Pinzani | first3=R. | title=Vexillary involutions are enumerated by Motzkin numbers | doi=10.1007/PL00001297 | mr=1904383 | year=2001 | journal=Annals of Combinatorics | issn=0218-0006 | volume=5 | issue=2 | pages=153–174}}
- {{Citation | last1=Lascoux | first1=Alain | last2=Schützenberger | first2=Marcel-Paul | title=Polynômes de Schubert | mr=660739 | year=1982 | journal=Comptes Rendus de l'Académie des Sciences, Série I | issn=0249-6291 | volume=294 | issue=13 | pages=447–450}}
- {{Citation | last1=Lascoux | first1=Alain | last2=Schützenberger | first2=Marcel-Paul | title=Schubert polynomials and the Littlewood–Richardson rule | doi=10.1007/BF00398147 | mr=815233 | year=1985 | journal=Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics | issn=0377-9017 | volume=10 | issue=2 | pages=111–124| bibcode=1985LMaPh..10..111L }}
- {{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}}