Unavoidable subprojections in union-closed set systems of infinite breadth

Yemon Choi; Mahya Ghandehari; Hung Le Pham

doi:10.1016/j.ejc.2021.103311

Unavoidable subprojections in union-closed set systems of infinite breadth

Combinatorics 2021-03-30 v6 Functional Analysis Group Theory

Authors: Yemon Choi , Mahya Ghandehari , Hung Le Pham

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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.

Keywords

set theory and dimension theory projective geometry combinatorial group theory

Cite

@article{arxiv.1702.06266,
  title  = {Unavoidable subprojections in union-closed set systems of infinite breadth},
  author = {Yemon Choi and Mahya Ghandehari and Hung Le Pham},
  journal= {arXiv preprint arXiv:1702.06266},
  year   = {2021}
}

Comments

v5: AMS LaTeX, 21 pages, 1 figure (tikz); uses the stmaryrd fonts. Incorporates referees' feedback. v6: updated to include two minor corrections found after acceptance, which are both included in the final published version. To appear in European J. Combin

Unavoidable subprojections in union-closed set systems of infinite breadth

Abstract

Keywords

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