Unavoidable subprojections in union-closed set systems of infinite breadth. (May 2021)

• Record Type: Journal Article
• Authors: Choi, Yemon; Ghandehari, Mahya; Pham, Hung Le
• Is Part Of: European journal of combinatorics. Volume 94(2021)
• Publication Date: 2021-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2021.103311
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We consider union-closed set systems with infinite breadth, focusing on three particular configurations T max ( E ), T min ( E ) and T ort ( E ) . We show that these three configurations are not isolated examples; in any given union-closed set system of infinite breadth, at least one of these three configurations will occur as a subprojection. This characterizes those union-closed set systems which have infinite breadth, and is the first general structural result for such set systems.