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dc.contributor.authorStanley, Richard P.
dc.contributor.authorZanello, Fabrizio
dc.date.accessioned2012-07-17T19:03:28Z
dc.date.available2012-07-17T19:03:28Z
dc.date.issued2012-04
dc.date.submitted2011-11
dc.identifier.issn1097-1440
dc.identifier.issn1077-8926
dc.identifier.urihttp://hdl.handle.net/1721.1/71661
dc.description.abstractWe study r-differential posets, a class of combinatorial objects introduced in 1988 by the first author, which gathers together a number of remarkable combinatorial and algebraic properties, and generalizes important examples of ranked posets, including the Young lattice. We first provide a simple bijection relating differential posets to a certain class of hypergraphs, including all finite projective planes, which are shown to be naturally embedded in the initial ranks of some differential poset. As a byproduct, we prove the existence, if and only if r≥6, of r-differential posets nonisomorphic in any two consecutive ranks but having the same rank function. We also show that the Interval Property, conjectured by the second author and collaborators for several sequences of interest in combinatorics and combinatorial algebra, in general fails for differential posets. In the second part, we prove that the rank function p[subscript n] of any arbitrary r-differential poset has nonpolynomial growth; namely, ... a bound very close to the Hardy-Ramanujan asymptotic formula that holds in the special case of Young's lattice. We conclude by posing several open questions.en_US
dc.description.sponsorshipMassachusetts Institute of Technology. Dept. of Mathematicsen_US
dc.language.isoen_US
dc.publisherInternational Pressen_US
dc.relation.isversionofhttp://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i2p13en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourcearXiven_US
dc.titleOn the rank function of a differential poseten_US
dc.typeArticleen_US
dc.identifier.citationStanley, Richard P. and Fabrizio Zanello. "On the rank function of a differential poset." Electronic Journal of Combinatorics (2012) 19.2, p.1-17.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.approverStanley, Richard P.
dc.contributor.mitauthorStanley, Richard P.
dc.relation.journalElectronic Journal of Combinatoricsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsStanley, Richard P.; Zanello, Fabrizio.en_US
dc.identifier.orcidhttps://orcid.org/0000-0003-3123-8241
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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