{"pk":64991,"title":"Asymptotic distribution of parameters in trivalent maps and linear lambda terms","subtitle":null,"abstract":"In this work, we study the limit distributions of various combinatorial parameters in trivalent maps, linear \\(\\lambda\\)-terms, and other related families of objects. We focus on parameters in maps which naturally correspond to parameters in \\(\\lambda\\)-terms and vice versa, allowing us to employ techniques from map theory and the \\(\\lambda\\)-calculus in a combinatorial interplay. Some examples of the parameters we study are: the number of bridges in rooted trivalent maps and of subterms in closed linear \\(\\lambda\\)-terms as well as the number of vertices of degree 1 in \\((1,3)\\)-valent maps and of free variables in open linear \\(\\lambda\\)-terms. To analyse their distributions, we introduce appropriate tools: a moment-pumping schema for differential equations and a composition schema inspired by Bender's theorem.\n \nMathematics Subject Classifications: 05A16, 05A19, 03B40, 05C30\n \nKeywords: Random maps on surfaces, lambda calculus, analytic combinatorics, limit laws","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":"Random maps on surfaces"},{"word":"lambda calculus"},{"word":"analytic combinatorics"},{"word":"limit laws"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/95k4f8wv","frozenauthors":[{"first_name":"Olivier","middle_name":"","last_name":"Bodini","name_suffix":"","institution":"EREN, Université Sorbonne Paris Nord, 93430 Villetaneuse, France","department":""},{"first_name":"Alexandros","middle_name":"","last_name":"Singh","name_suffix":"","institution":"LIASD, Université Paris 8, 93200 Saint-Denis, France","department":""},{"first_name":"Noam","middle_name":"","last_name":"Zeilberger","name_suffix":"","institution":"LIX, École Polytechnique, 91120 Palaiseau, France","department":""}],"date_submitted":"2025-07-15T08:27:29-07:00","date_accepted":"2025-07-15T08:27:29-07:00","date_published":"2025-07-15T00:00:00-07:00","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64991/galley/49801/download/"}]}