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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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Unavoidable subprojections in union-closed set systems of infinite breadth. / Choi, Yemon; Ghandehari, Mahya; Pham, Hung Le.
In: European Journal of Combinatorics, Vol. 94, 103311, 01.05.2021.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Choi, Y, Ghandehari, M & Pham, HL 2021, 'Unavoidable subprojections in union-closed set systems of infinite breadth', European Journal of Combinatorics, vol. 94, 103311. https://doi.org/10.1016/j.ejc.2021.103311

APA

Choi, Y., Ghandehari, M., & Pham, H. L. (2021). Unavoidable subprojections in union-closed set systems of infinite breadth. European Journal of Combinatorics, 94, Article 103311. https://doi.org/10.1016/j.ejc.2021.103311

Vancouver

Choi Y, Ghandehari M, Pham HL. Unavoidable subprojections in union-closed set systems of infinite breadth. European Journal of Combinatorics. 2021 May 1;94:103311. Epub 2021 Feb 19. doi: 10.1016/j.ejc.2021.103311

Author

Choi, Yemon ; Ghandehari, Mahya ; Pham, Hung Le. / Unavoidable subprojections in union-closed set systems of infinite breadth. In: European Journal of Combinatorics. 2021 ; Vol. 94.

Bibtex

@article{2c965a55f69a4ab5842da0bc1f04ad5a,
title = "Unavoidable subprojections in union-closed set systems of infinite breadth",
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 = "Semilattice, breadth, union-closed set system, subprojection",
author = "Yemon Choi and Mahya Ghandehari and Pham, {Hung Le}",
note = "This is the author{\textquoteright}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",
year = "2021",
month = may,
day = "1",
doi = "10.1016/j.ejc.2021.103311",
language = "English",
volume = "94",
journal = "European Journal of Combinatorics",
issn = "0195-6698",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Unavoidable subprojections in union-closed set systems of infinite breadth

AU - Choi, Yemon

AU - Ghandehari, Mahya

AU - Pham, Hung Le

N1 - 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

PY - 2021/5/1

Y1 - 2021/5/1

N2 - 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.

AB - 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.

KW - Semilattice

KW - breadth

KW - union-closed set system

KW - subprojection

U2 - 10.1016/j.ejc.2021.103311

DO - 10.1016/j.ejc.2021.103311

M3 - Journal article

VL - 94

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

M1 - 103311

ER -