{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T12:38:20Z","timestamp":1778589500344,"version":"3.51.4"},"reference-count":42,"publisher":"American Mathematical Society (AMS)","issue":"307","license":[{"start":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T00:00:00Z","timestamp":1511827200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang\u2013Baxter equation. We generalize Rump\u2019s braces to the non-commutative setting and use this new structure to study not necessarily involutive non-degenerate set-theoretical solutions of the Yang\u2013Baxter equation. Based on results of Bachiller and Catino and Rizzo, we develop an algorithm to enumerate and construct classical and non-classical braces of small size up to isomorphism. This algorithm is used to produce a database of braces of small size. The paper contains several open problems, questions and conjectures.<\/p>","DOI":"10.1090\/mcom\/3161","type":"journal-article","created":{"date-parts":[[2016,3,23]],"date-time":"2016-03-23T14:52:55Z","timestamp":1458744775000},"page":"2519-2534","source":"Crossref","is-referenced-by-count":223,"title":["Skew braces and the Yang\u2013Baxter equation"],"prefix":"10.1090","volume":"86","author":[{"given":"L.","family":"Guarnieri","sequence":"first","affiliation":[]},{"given":"L.","family":"Vendramin","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2016,11,28]]},"reference":[{"issue":"8","key":"1","doi-asserted-by":"publisher","first-page":"3568","DOI":"10.1016\/j.jpaa.2014.12.013","article-title":"Classification of braces of order \ud835\udc5d\u00b3","volume":"219","author":"Bachiller, David","year":"2015","journal-title":"J. Pure Appl. 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