{"pk":64905,"title":"Tilings of benzels via the abacus bijection","subtitle":null,"abstract":"Propp recently introduced regions in the hexagonal grid called benzels and stated several enumerative conjectures about the tilings of benzels using two types of prototiles called stones and bones. We resolve two of his conjectures and prove some additional results that he left tacit. In order to solve these problems, we first transfer benzels into the square grid. One of our primary tools, which we combine with several new ideas, is a bijection (rediscovered by Stanton and White and often attributed to them although it is considerably older) between \\(k\\)-ribbon tableaux of certain skew shapes and certain \\(k\\)-tuples of Young tableaux.\n \nMathematics Subject Classifications: 05B45, 05A15, 05A17\n \nKeywords: Tiling, benzel, abacus bijection, core partition, domino, stone, bone","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":"Tiling"},{"word":"benzel"},{"word":"abacus bijection"},{"word":"core partition"},{"word":"domino"},{"word":"stone"},{"word":"bone"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/5h16p4t1","frozenauthors":[{"first_name":"Colin","middle_name":"","last_name":"Defant","name_suffix":"","institution":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.","department":""},{"first_name":"Rupert","middle_name":"","last_name":"Li","name_suffix":"","institution":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.","department":""},{"first_name":"James","middle_name":"","last_name":"Propp","name_suffix":"","institution":"Department of Mathematical Sciences, UMass Lowell, Lowell, MA 01854, U.S.A.","department":""},{"first_name":"Benjamin","middle_name":"","last_name":"Young","name_suffix":"","institution":"Department of Mathematics, University of Oregon, Eugene OR 97403, U.S.A.","department":""}],"date_submitted":"2023-09-14T08:23:47Z","date_accepted":"2023-09-14T08:23:47Z","date_published":"2023-09-15T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64905/galley/49715/download/"}]}