{"pk":64882,"title":"Packings and Steiner systems in polar spaces","subtitle":null,"abstract":"A finite classical polar space of rank \\(n\\) consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that \\(n\\) is the maximal dimension of such a subspace. A \\(t\\)-Steiner system in a finite classical polar space of rank \\(n\\) is a collection \\(Y\\) of totally isotropic \\(n\\)-spaces such that each totally isotropic \\(t\\)-space is contained in exactly one member of \\(Y\\). Nontrivial examples are known only for \\(t=1\\) and \\(t=n-1\\). We give an almost complete classification of such \\(t\\)-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces.\n \nMathematics Subject Classifications: 51E23, 05E30, 33C80\n \nKeywords: Association schemes, codes, polar spaces, Steiner systems","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":"Association schemes"},{"word":"codes"},{"word":"polar spaces"},{"word":"Steiner systems"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/83g3149p","frozenauthors":[{"first_name":"Kai-Uwe","middle_name":"","last_name":"Schmidt","name_suffix":"","institution":"Department of Mathematics, Paderborn University, Paderborn, Germany","department":""},{"first_name":"Charlene","middle_name":"","last_name":"Weiß","name_suffix":"","institution":"Department of Mathematics, Paderborn University, Paderborn, Germany","department":""}],"date_submitted":"2023-03-14T16:07:58Z","date_accepted":"2023-03-14T16:07:58Z","date_published":"2023-03-15T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64882/galley/49692/download/"}]}