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On the Density of Sets Containing No k ‐Element Arithmetic Progression of a Certain Kind
Author(s) -
Alspach Brian,
Brown T. C.,
Hell Pavol
Publication year - 1976
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-13.2.226
Subject(s) - citation , columbia university , mathematics , library science , history , computer science , media studies , sociology
A theorem now known as Sperner's Lemma [5] states that a largest collection of subsets of an n-element set such that no subset contains another is obtained by taking the collection of all the subsets with cardinal [n/2\. (We denote by |*J, resp. [*], the largest integer less than or equal to x, resp. the smallest integer greater than or equal to x.) In other words, the density of a largest antichain in the set of all subsets of an w-element set is