{"pk":65043,"title":"Two gluing methods for string C-group representations of the symmetric groups","subtitle":null,"abstract":"The study of string C-group representations of rank at least \\(n/2\\) for the symmetric group \\(S_n\\) has gained a lot of attention in the last fifteen years. In a recent paper, Cameron et al. gave a list of permutation representation graphs of rank \\(r\\geq n/2\\) for \\(S_n\\), having a fracture graph and a non-perfect split. They conjecture that these graphs are permutation representation graphs of string C-groups. In trying to prove this conjecture, we discovered two new techniques to glue two CPR graphs for symmetric groups together. We discuss the cases in which they yield new CPR graphs. By doing so, we invalidate the conjecture of Cameron et al. We believe our gluing techniques will be useful in the study of string C-group representations of high ranks for the symmetric groups.\n \nMathematics Subject Classifications: 20B30, 05C25, 52B15\n \nKeywords: String C-group representations, symmetric groups, permutation representation graphs, CPR graphs","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":"String C-group representations"},{"word":"symmetric groups"},{"word":"permutation representation graphs"},{"word":"CPR graphs"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/1qn7796p","frozenauthors":[{"first_name":"Dimitri","middle_name":"","last_name":"Leemans","name_suffix":"","institution":"Département de Mathématique, Université libre de Bruxelles, C.P.216, Boulevard du Triomphe, 1050 Brussels, Belgium","department":""},{"first_name":"Jessica","middle_name":"","last_name":"Mulpas","name_suffix":"","institution":"Département de Mathématique, Université libre de Bruxelles, C.P.216, Boulevard du Triomphe, 1050 Brussels, Belgium","department":""}],"date_submitted":"2026-04-20T19:47:55Z","date_accepted":"2026-04-20T19:47:55Z","date_published":"2026-04-20T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/65043/galley/49853/download/"}]}