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大连理工大学学报 2009
PosetonDyckpathsDOI: 10.7511/dllgxb200906037, PP. 995-1000 Keywords: Dyckpath,poset,Whitneynumber,Mbiusfunction,Hassediagram Abstract: ADyckpathisthelatticepathinthefirstquadrantconsistingofupstepsanddownsteps.TheposetonDyckpathscanbeorderedbyinclusion,whichisadistributivelattice.TheWhitneynumberoftheposetsatisfiesarecurrenceanditsgeneratingfunctioncanbewrittenasacontinuedfraction.Thejoin-irreduciblesoftheposetareisomorphictotheposetofinternalsofn-elementchain.TheMbiusfunctionoftheposetisgivenanditsapplicationsarediscussed.TheHassediagramoftheposetisconstructedrecursivelybyusingECOmethod.Finally,anotherkindofposetontheDyckpathsisintroduced,i.e.,theorderrelationisdefinedbyinclusionaswellasthenumberofpeaks.
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