Statistics on permutation tableaux

Pawel Hitczenko

Description

Statistics on permutation tableaux Pawel Hitczenko Drexel University parts based on joint work with Sylvie Corteel (Paris-Sud) and parts with Svante Janson (Uppsala) LIPN, February 5, 2008

• length ?


• svante janson


• columns ?


• paris sud


• permutation tableau


• partition ?

Sujets

• Drexel University
• Svante Janson

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 14
• Langue: English

Extrait

Statisticsonpermutationtableaux PawelHitczenko DrexelUniversity partsbasedonjointworkwithSylvieCorteel(Paris-Sud) andpartswithSvanteJanson(Uppsala) LIPN,February5,2008

Permutationtableaux Permutationtableau T :aFerrersdiagramofapartitionλfilled with0’sand1’ssuchthat: 1.Eachcolumncontainsatleastone1. 2.Thereisno0whichhasa1aboveitinthesamecolumn and a1toitsleftinthesamerow. 0010011 0 0 1 01 1 0 1 1 1 000 1

Previouswork ◮ introducedbyPostnikov(2001) ◮ subsequentlystudiedbyWilliams(2004),Steingrı´mssonand Williams(2005)(bijectionswithpermutations) ◮ connectionstoPASEP(aparticlemodelinstatisticalphysics) CorteelandWilliams(2006)and(2007). ◮ additionalcombinatorialworkCorteelandNadeau(2007) (morebijections),Burstein(2006)(somepropertiesof permutationtableaux)

Statisticson T ◮ Lengthℓ( T ):no.rowsplusno.columns 0 0 0 0 1 0 0 1 0 1 1 0 0 1 011 111 0 ℓ( T )=12 Numberofpermutationtableauxoflengthn=n!. allpermutationtableauxwithℓ(T)=n. T n isthesetof

Statisticson T ◮ Lengthℓ( T ):no.rowsplusno.columns ◮ U ( T ):numberofunrestrictedrows(arowisrestrictedifit hasa0thathas1aboveit) → → → → 0 0 0 0 1 1 0 0 0 1 11 0 0 0 11 0 11 1 U ( T )=4