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Path Counting and Rank Gaps in Differential Posets
| dc.contributor.author | Gaetz, Christian | |
| dc.contributor.author | Venkataramana, Praveen | |
| dc.date.accessioned | 2021-09-20T17:30:09Z | |
| dc.date.available | 2021-09-20T17:30:09Z | |
| dc.date.issued | 2019-09-21 | |
| dc.identifier.uri | https://hdl.handle.net/1721.1/131754 | |
| dc.description.abstract | Abstract We study the gaps Δpn between consecutive rank sizes in r-differential posets by introducing a projection operator whose matrix entries can be expressed in terms of the number of certain paths in the Hasse diagram. We strengthen Miller’s result that Δpn ≥ 1, which resolved a longstanding conjecture of Stanley, by showing that Δpn ≥ 2r. We also obtain stronger bounds in the case that the poset has many substructures called threads. | en_US |
| dc.publisher | Springer Netherlands | en_US |
| dc.relation.isversionof | https://doi.org/10.1007/s11083-019-09504-4 | en_US |
| dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
| dc.source | Springer Netherlands | en_US |
| dc.title | Path Counting and Rank Gaps in Differential Posets | en_US |
| dc.type | Article | 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 | 2020-09-24T20:35:22Z | |
| dc.language.rfc3066 | en | |
| dc.rights.holder | Springer Nature B.V. | |
| dspace.embargo.terms | Y | |
| dspace.date.submission | 2020-09-24T20:35:22Z | |
| mit.license | PUBLISHER_POLICY | |
| mit.metadata.status | Authority Work and Publication Information Needed |
