{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:27:20Z","timestamp":1761611240590},"reference-count":2,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T00:00:00Z","timestamp":1236124800000},"content-version":"unspecified","delay-in-days":5207,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[1994,12]]},"abstract":"<jats:p>The shuffle product of two words u and v, denoted u\u2016v, is the set of all words of the form <jats:italic>x<\/jats:italic><jats:sub>1<\/jats:sub><jats:italic>y<\/jats:italic><jats:sub>1<\/jats:sub><jats:italic>x<\/jats:italic><jats:sub>2<\/jats:sub><jats:italic>y<\/jats:italic><jats:sub>2<\/jats:sub>\u2026<jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub><jats:italic>y<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> for some n and for some (possible empty) words <jats:italic>x<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026<jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, <jats:italic>y<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026<jats:italic>y<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, such that <jats:italic>u<\/jats:italic> = <jats:italic>x<\/jats:italic><jats:sup>1<\/jats:sup><jats:italic>x<\/jats:italic><jats:sub>2<\/jats:sub>\u2026<jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, and <jats:italic>v<\/jats:italic> = <jats:italic>y<\/jats:italic><jats:sub>1<\/jats:sub><jats:italic>y<\/jats:italic><jats:sub>2<\/jats:sub>\u2026<jats:italic>y<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>. In other words, <jats:italic>u<\/jats:italic>\u2016<jats:italic>v<\/jats:italic> is the set of all possible words that can be obtained by merging <jats:italic>u<\/jats:italic> and <jats:italic>v<\/jats:italic> so that the letters of <jats:italic>u<\/jats:italic> and <jats:italic>v<\/jats:italic> separately maintain their original orders but are allowed to alternate arbitrarily. The shuffle product of languages <jats:italic>L<\/jats:italic> and <jats:italic>M<\/jats:italic>, denoted <jats:italic>L<\/jats:italic>\u2016<jats:italic>M<\/jats:italic>, is the union of all <jats:italic>u<\/jats:italic>\u2016<jats:italic>v<\/jats:italic> for <jats:italic>u<\/jats:italic> \u2208 <jats:italic>L<\/jats:italic> and <jats:italic>v<\/jats:italic> \u2208 <jats:italic>M<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0960129500000578","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T09:00:57Z","timestamp":1236157257000},"page":"505-511","source":"Crossref","is-referenced-by-count":8,"title":["Languages under concatenation and shuffling"],"prefix":"10.1017","volume":"4","author":[{"given":"Steven T.","family":"Tschantz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,4]]},"reference":[{"key":"S0960129500000578_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(88)90124-7"},{"key":"S0960129500000578_ref002","doi-asserted-by":"publisher","DOI":"10.1137\/0211023"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129500000578","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T21:55:10Z","timestamp":1557870910000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129500000578\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,12]]},"references-count":2,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,12]]}},"alternative-id":["S0960129500000578"],"URL":"https:\/\/doi.org\/10.1017\/s0960129500000578","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,12]]}}}