{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:24:47Z","timestamp":1775643887529,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5-6","license":[{"start":{"date-parts":[[2003,12,3]],"date-time":"2003-12-03T00:00:00Z","timestamp":1070409600000},"content-version":"unspecified","delay-in-days":32,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2003,11]]},"abstract":"<jats:p>Let \u03c3 be a finite relational signature, let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005765_inline1.png\"\/> be a set of finite complete relational structures of signature \u03c3, and let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005765_inline2.png\"\/> be the countable homogeneous relational structure of signature \u03c3 which does not embed any of the structures in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005765_inline1.png\"\/>.<\/jats:p><jats:p>When \u03c3 consists of at most binary relations and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005765_inline1.png\"\/> is finite, the vertex partition behaviour of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005765_inline2.png\"\/> is completely analysed, in the sense that it is shown that a canonical partition exists and the size of this partition in terms of the structures in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005765_inline1.png\"\/> is determined. If <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005765_inline1.png\"\/> is infinite some results are obtained, but a complete analysis is still missing.<\/jats:p><jats:p>Some general results are presented which are intended to be used in further investigations when \u03c3 contains relational symbols of arity larger than two or when the set of bounds <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0963548303005765_inline1.png\"\/> is infinite.<\/jats:p>","DOI":"10.1017\/s0963548303005765","type":"journal-article","created":{"date-parts":[[2003,12,3]],"date-time":"2003-12-03T14:23:14Z","timestamp":1070461394000},"page":"671-704","source":"Crossref","is-referenced-by-count":12,"title":["Canonical Vertex Partitions"],"prefix":"10.1017","volume":"12","author":[{"given":"N. W.","family":"Sauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2003,12,3]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548303005765","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T09:22:30Z","timestamp":1589534550000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548303005765\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,11]]},"references-count":0,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2003,11]]}},"alternative-id":["S0963548303005765"],"URL":"https:\/\/doi.org\/10.1017\/s0963548303005765","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,11]]}}}