{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T18:19:35Z","timestamp":1725473975299},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,2]]},"abstract":"<jats:p> This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen &amp; Qui and G\u00fczel Karpuz; we then construct biautomatic structures. For hypoplactic monoids, we construct finite complete rewriting systems and biautomatic structures. For sylvester monoids, which are not finitely presented, we prove that the standard presentation is an infinite complete rewriting system, and construct biautomatic structures. Consequently, the monoid algebras corresponding to monoids of these classes are automaton algebras in the sense of Ufnarovskij. <\/jats:p>","DOI":"10.1142\/s0218196715400044","type":"journal-article","created":{"date-parts":[[2015,1,9]],"date-time":"2015-01-09T08:33:15Z","timestamp":1420792395000},"page":"51-80","source":"Crossref","is-referenced-by-count":8,"title":["Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids"],"prefix":"10.1142","volume":"25","author":[{"given":"Alan J.","family":"Cain","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, 2829\u2013516 Caparica, Portugal"}]},{"given":"Robert D.","family":"Gray","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK"}]},{"given":"Ant\u00f3nio","family":"Malheiro","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, 2829\u2013516 Caparica, Portugal"},{"name":"Centro de \u00c1lgebra da Universidade de Lisboa, Av. 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