On the existence of regular antichains

A k-regular antichain in the Boolean lattice of subsets is one in which each point occurs in exactly k sets. The existence and construction of k-regular antichains on m points for each positive integer pair (k,m) is determined for all m and most k.

Saved in:
Bibliographic Details
Published inDiscrete mathematics Vol. 313; no. 4; pp. 348 - 356
Main Authors Roberts, Ian T., Böhm, Matthias
Format Journal Article
LanguageEnglish
Published Elsevier B.V 28.02.2013
Subjects
Completely separating systems
Extremal set theory
Regular antichain
Sperner theory
Regular antichain
Completely separating systems
Sperner theory
Extremal set theory
Online AccessGet full text

Cover

More Information
Summary:A k-regular antichain in the Boolean lattice of subsets is one in which each point occurs in exactly k sets. The existence and construction of k-regular antichains on m points for each positive integer pair (k,m) is determined for all m and most k.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2012.10.022