{"pk":64932,"title":"Sets of mutually orthogoval projective and affine planes","subtitle":null,"abstract":"A pair of planes, both projective or both affine, of the same order and on the same point set are orthogoval if each line of one plane intersects each line of the other plane in at most two points. In this paper we prove new constructions for sets of mutually orthogoval planes, both projective and affine, and review known results that are equivalent to sets of more than two mutually orthogoval planes. We also discuss the connection between sets of mutually orthogoval planes and covering arrays.\n \nMathematics Subject Classifications: 05B25, 05B40, 51E20, 51E21\n \nKeywords: Finite geometry, projective planes, affine planes, covering arrays, orthogoval planes","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":"Finite geometry"},{"word":"projective planes"},{"word":"affine planes"},{"word":"covering arrays"},{"word":"orthogoval planes"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/6q20z7sg","frozenauthors":[{"first_name":"Charles","middle_name":"J.","last_name":"Colbourn","name_suffix":"","institution":"School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ 85287-8809, U.S.A.","department":""},{"first_name":"Colin","middle_name":"","last_name":"Ingalls","name_suffix":"","institution":"School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada","department":""},{"first_name":"Jonathan","middle_name":"","last_name":"Jedwab","name_suffix":"","institution":"Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada","department":""},{"first_name":"Mark","middle_name":"","last_name":"Saaltink","name_suffix":"","institution":"Independent researcher","department":""},{"first_name":"Ken","middle_name":"W.","last_name":"Smith","name_suffix":"","institution":"Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX 77341, U.S.A.","department":""},{"first_name":"Brett","middle_name":"","last_name":"Stevens","name_suffix":"","institution":"School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa ON K1S 5B6, Canada","department":""}],"date_submitted":"2024-07-01T09:50:50Z","date_accepted":"2024-07-01T09:50:50Z","date_published":"2024-06-30T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64932/galley/49742/download/"}]}