Statistics on permutation tableaux

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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 ?


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StatisticsonpermutationtableauxPawelHitczenkoDrexelUniversitypartsbasedonjointworkwithSylvieCorteel(Paris-Sud)andpartswithSvanteJanson(Uppsala)LIPN,February5,2008
PermutationtableauxPermutationtableauT:aFerrersdiagramofapartitionλfilledwith0’sand1’ssuchthat:1.Eachcolumncontainsatleastone1.2.Thereisno0whichhasa1aboveitinthesamecolumnanda1toitsleftinthesamerow.001001100101101110001
PreviousworkintroducedbyPostnikov(2001)subsequentlystudiedbyWilliams(2004),Steingrı´mssonandWilliams(2005)(bijectionswithpermutations)connectionstoPASEP(aparticlemodelinstatisticalphysics)CorteelandWilliams(2006)and(2007).additionalcombinatorialworkCorteelandNadeau(2007)(morebijections),Burstein(2006)(somepropertiesofpermutationtableaux)
StatisticsonTLength(T):no.rowsplusno.columns000010010110010111110(T)=12Numberofpermutationtableauxoflengthn=n!.allpermutationtableauxwith(T)=n.Tnisthesetof
StatisticsonTLength(T):no.rowsplusno.columnsU(T):numberofunrestrictedrows(arowisrestrictedifithasa0thathas1aboveit)000011000111000110111U(T)=4