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    Rights statement: This is the author’s version of a work that was accepted for publication in European Journal of Combinatorics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Combinatorics, 94, 2021 DOI: 10.1016/j.ejc.2021.103311

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Unavoidable subprojections in union-closed set systems of infinite breadth

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Article number103311
<mark>Journal publication date</mark>1/05/2021
<mark>Journal</mark>European Journal of Combinatorics
Volume94
Number of pages17
Publication StatusE-pub ahead of print
Early online date19/02/21
<mark>Original language</mark>English

Abstract

We consider union-closed set systems with infinite breadth, focusing on three particular configurations ${\mathcal T}_{\rm max}(E)$, ${\mathcal T}_{\rm min}(E)$ and ${\mathcal T}_{\rm ort}(E)$. 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.

Bibliographic note

This is the author’s version of a work that was accepted for publication in European Journal of Combinatorics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Combinatorics, 94, 2021 DOI: 10.1016/j.ejc.2021.103311