A generalization of Hanani's theorem on partial order

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1983 Germany English Publisher:Springer Science and Business Media LLCJournal:Monatshefte f�r Mathematik, volume 95, pages 177-179 (issn: 0026-9255, eissn: 1436-5081,

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Authors: Burkill, H.; Smallwood, Catherine V.;

doi: 10.1007/bf01351995

A generalization of Hanani's theorem on partial order

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Abstract

The theorem of Hanani referred to in the title of this note states that, if a partially ordered set has cardinal not exceeding 1/2n(n+3) (n=1,2,...), then it can be expressed as the union ofn sets each of which is either a chain or an antichain. A corresponding result is now obtained for a set equipped with an arbitrary number of partial order relations.

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Keywords

partially ordered set, 510.mathematics, Partial orders, general, union of extreme sets, chains, Exact enumeration problems, generating functions, antichains, Article

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