PDF-ReducedDecompositionsRichardP.StanleyM.I.T.ReducedDecompositions
Author : jane-oiler | Published Date : 2016-11-15
DenitionsAdjacenttranspositionsiii12Sn1in1reduceddecompositiona1apofw2Snwsa1sapwherepisminimaliepwfijijwiwjgpisthenumberofinversionsinvworlengthwofwR
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ReducedDecompositionsRichardP.StanleyM.I.T.ReducedDecompositions: Transcript
DenitionsAdjacenttranspositionsiii12Sn1in1reduceddecompositiona1apofw2Snwsa1sapwherepisminimaliepwfijijwiwjgpisthenumberofinversionsinvworlengthwofwR. StandardYoungtableaustandardYoungtableau(SYT)ofshape=(4;4;3;1):8910521312114HookLengthsandContents BasicdenitionsAsequencea1;a2;:::;akofdistinctintegersisalternatingifa1 a2a3 a4;andreversealternatingifa1a2 a3a4 :AlternatingPermutations RichardP.StanleyM.I.T. AChromaticSymmetricFunctionConjecture Despitesuccessesinreducingtheamountofrework,itisgenerallyacceptedthatreworkcannotbeeliminatedentirely.Moreover,notallrework-inducingproblemscanbedetectedassoonastheyoccur;someproblemswillonlybecaughts Denitions318496725(i:s)318496725(d:s)is(w)=jlongesti:s:j=4ds(w)=jlongestd:s:j=3IncreasingandDecreasingSubsequences
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