| dc.contributor.author | Liu, Fu | |
| dc.contributor.author | Stanley, Richard P | |
| dc.date.accessioned | 2016-10-06T22:10:23Z | |
| dc.date.available | 2016-10-06T22:10:23Z | |
| dc.date.issued | 2014-10 | |
| dc.date.submitted | 2013-12 | |
| dc.identifier.issn | 1382-4090 | |
| dc.identifier.issn | 1572-9303 | |
| dc.identifier.uri | http://hdl.handle.net/1721.1/104774 | |
| dc.description.abstract | Let T be a collection of 3-element subsets S of {1,…,n} with the property that if i<j<k and a<b<c are two 3-element subsets in S, then there exists an integer sequence x[subscript 1]<x[subscript 2]<⋯<x[subscript n] such that x[subscript i],x[subscript j],x[subscript k] and x[subscript a],x[subscript b],x[subscript c] are arithmetic progressions. We determine the number of such collections T and the number of them of maximum size. These results confirm two conjectures of Noam Elkies. | en_US |
| dc.description.sponsorship | National Science Foundation (U.S.) (Grant DMS-1068625) | en_US |
| dc.publisher | Springer US | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1007/s11139-014-9623-2 | en_US |
| dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
| dc.source | Springer US | en_US |
| dc.title | A distributive lattice connected with arithmetic progressions of length three | en_US |
| dc.type | Article | en_US |
| dc.identifier.citation | Liu, Fu, and Richard P. Stanley. “A Distributive Lattice Connected with Arithmetic Progressions of Length Three.” The Ramanujan Journal 36.1–2 (2015): 203–226. | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
| dc.contributor.mitauthor | Stanley, Richard P | |
| dc.relation.journal | The Ramanujan Journal | en_US |
| dc.eprint.version | Author's final manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
| dc.date.updated | 2016-08-18T15:45:00Z | |
| dc.language.rfc3066 | en | |
| dc.rights.holder | Springer Science+Business Media New York | |
| dspace.orderedauthors | Liu, Fu; Stanley, Richard P. | en_US |
| dspace.embargo.terms | N | en |
| dc.identifier.orcid | https://orcid.org/0000-0003-3123-8241 | |
| mit.license | OPEN_ACCESS_POLICY | en_US |
| mit.metadata.status | Complete | |
