PDF-HookLengthsandContentsRichardP.StanleyM.I.T.HookLengthsandContents
Author : sherrill-nordquist | Published Date : 2016-04-24
StandardYoungtableaustandardYoungtableauSYTofshape44318910521312114HookLengthsandContents
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HookLengthsandContentsRichardP.StanleyM.I.T.HookLengthsandContents: Transcript
StandardYoungtableaustandardYoungtableauSYTofshape44318910521312114HookLengthsandContents. BasicdenitionsAsequencea1;a2;:::;akofdistinctintegersisalternatingifa1 a2a3 a4;andreversealternatingifa1a2 a3a4 :AlternatingPermutations RichardP.StanleyM.I.T. AChromaticSymmetricFunctionConjecture Despitesuccessesinreducingtheamountofrework,itisgenerallyacceptedthatreworkcannotbeeliminatedentirely.Moreover,notallrework-inducingproblemscanbedetectedassoonastheyoccur;someproblemswillonlybecaughts DenitionsAdjacenttransposition:si=(i;i+1)2Sn;1in 1reduceddecomposition(a1;:::;ap)ofw2Sn:w=sa1sap;wherepisminimal,i.e.,p=`(w)=#f(i;j):ij;w(i) w(j)g:pisthenumberofinversionsinv(w)orlength`(w)ofw.R Denitions318496725(i:s)318496725(d:s)is(w)=jlongesti:s:j=4ds(w)=jlongestd:s:j=3IncreasingandDecreasingSubsequences
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