{"pk":64849,"title":"A note on saturation for $k$-wise intersecting families","subtitle":null,"abstract":"A family $\\mathcal{F}$ of subsets of $\\{1,\\dots,n\\}$ is called $k$-wise intersecting if any $k$ members of $\\mathcal{F}$ have non-empty intersection, and it is called maximal $k$-wise intersecting if no family strictly containing $\\mathcal{F}$ satisfies this condition. We show that for each $k\\geq 2$ there is a maximal $k$-wise intersecting family of size $O(2^{n/(k-1)})$. Up to a constant factor, this matches the best known lower bound, and answers an old question of Erdős and Kleitman, recently studied by Hendrey, Lund, Tompkins, and Tran.\n \nMathematics Subject Classifications: 05D05\n \nKeywords: Intersecting family, saturation, set system","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Intersecting family"},{"word":"saturation"},{"word":"set system"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/30f8m0xh","frozenauthors":[{"first_name":"Barnabás","middle_name":"","last_name":"Janzer","name_suffix":"","institution":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, United Kingdom","department":""}],"date_submitted":"2022-06-25T19:42:09Z","date_accepted":"2022-06-25T19:42:09Z","date_published":"2022-06-30T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64849/galley/49659/download/"}]}