{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:44:34Z","timestamp":1740120274260,"version":"3.37.3"},"reference-count":40,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"AGIRA","award":["ANR-16-CE40-0022-01"],"award-info":[{"award-number":["ANR-16-CE40-0022-01"]}]},{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"crossref","award":["296018"],"award-info":[{"award-number":["296018"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p> The growth of a finitely generated group is an important geometric invariant which has been studied for decades. It can be either polynomial, for a well-understood class of groups, or exponential, for most groups studied by geometers, or intermediate, that is between polynomial and exponential. Despite recent spectacular progresses, the class of groups with intermediate growth remains largely mysterious. Many examples of such groups are constructed using Mealy automata. The aim of this paper is to give an algorithmic procedure to study the growth of such automaton groups, and more precisely to provide numerical upper bounds on their exponents. Our functions retrieve known optimal bounds on the famous first Grigorchuk group. They also improve known upper bounds on other automaton groups and permitted us to discover several new examples of automaton groups of intermediate growth. All the algorithms described are implemented in GAP, a language dedicated to computational group theory. <\/jats:p>","DOI":"10.1142\/s0218196722500072","type":"journal-article","created":{"date-parts":[[2021,11,5]],"date-time":"2021-11-05T01:13:50Z","timestamp":1636074830000},"page":"159-191","source":"Crossref","is-referenced-by-count":0,"title":["Numerical upper bounds on growth of automaton groups"],"prefix":"10.1142","volume":"32","author":[{"given":"J\u00e9r\u00e9mie","family":"Brieussel","sequence":"first","affiliation":[{"name":"IMAG, UMR 5149 CNRS & Universit\u00e9 de Montpellier, France"}]},{"given":"Thibault","family":"Godin","sequence":"additional","affiliation":[{"name":"IMAG, UMR 5149 CNRS & Universit\u00e9 de Montpellier, France"},{"name":"IECL, UMR 7502 CNRS & Universit\u00e9 de Lorraine, France"}]},{"given":"Bijan","family":"Mohammadi","sequence":"additional","affiliation":[{"name":"IMAG, UMR 5149 CNRS & Universit\u00e9 de Montpellier, France"}]}],"member":"219","published-online":{"date-parts":[[2021,11,3]]},"reference":[{"key":"S0218196722500072BIB001","doi-asserted-by":"publisher","DOI":"10.1155\/S1073792898000622"},{"key":"S0218196722500072BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(03)00131-6"},{"key":"S0218196722500072BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-34171-2_3"},{"key":"S0218196722500072BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-011-0368-x"},{"key":"S0218196722500072BIB006","doi-asserted-by":"publisher","DOI":"10.5802\/aif.2902"},{"key":"S0218196722500072BIB007","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-100106794"},{"key":"S0218196722500072BIB008","doi-asserted-by":"publisher","DOI":"10.4171\/GGD\/184"},{"key":"S0218196722500072BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-008-0417-3"},{"key":"S0218196722500072BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s13370-013-0182-2"},{"key":"S0218196722500072BIB011","doi-asserted-by":"publisher","DOI":"10.1515\/jgth-2017-0046"},{"key":"S0218196722500072BIB012","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2004.160.1183"},{"key":"S0218196722500072BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-019-00922-0"},{"key":"S0218196722500072BIB014","first-page":"217","volume":"56","author":"Fabrikowsky J.","year":"1991","journal-title":"J. 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