Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/23502
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dc.contributor.authorWong, Willie Han Wahen
dc.contributor.authorTay, Eng Guanen
dc.date.accessioned2021-12-03T02:09:45Z-
dc.date.available2021-12-03T02:09:45Z-
dc.date.issued2022-
dc.identifier.citationWong, H. W., & Tay, E. G. (2022). Kruskal-katona function and variants of cross-intersecting antichains. Discrete Mathematics, 345(3), Article 112709. https://doi.org/10.1016/j.disc.2021.112709en
dc.identifier.issn0012-365X-
dc.identifier.urihttp://hdl.handle.net/10497/23502-
dc.description.abstractWe prove some properties of the Kruskal-Katona function and apply to the following variant of cross-intersecting antichains. Let n ≥ 4 be an even integer and A and B be two cross-intersecting antichains on [n] with at most k disjoint pairs, i.e., for all Ai ∈ A , Bj ∈ B, Ai ∩ Bj = ∅ only if i = j ≤ k. We prove a best possible upper bound on |A |+|B| and show that the extremal families contain only <math><mfrac is="true"><mrow is="true"><mi is="true">n</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></mfrac></math> and <math><mo stretchy="false" is="true">(</mo><mfrac is="true"><mrow is="true"><mi is="true">n</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></mfrac><mo linebreak="badbreak" linebreakstyle="after" is="true">+</mo><mn is="true">1</mn><mo stretchy="false" is="true">)</mo></math>-sets. The main tools are Sperner operations and Kruskal-Katona’s Theorem.en
dc.language.isoenen
dc.relation.ispartofDiscrete Mathematicsen
dc.subjectKruskal-Katonaen
dc.subjectSperner familiesen
dc.subjectAntichainsen
dc.subjectSperner operationsen
dc.subjectCross-intersectingen
dc.titleKruskal-Katona function and variants of cross-intersecting antichainsen
dc.typeArticleen
dc.description.versionAccepted versionen
dc.identifier.doi10.1016/j.disc.2021.112709-
local.message.claim2021-12-23T13:08:32.314+0800|||rp00125|||submit_approve|||dc_contributor_author|||None*
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextWith file-
item.languageiso639-1en-
item.openairetypeArticle-
item.grantfulltextEmbargo_20240401-
item.cerifentitytypePublications-
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