{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:23Z","timestamp":1753894403448,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In this paper we investigate the interplay between isolated suborders and\nclosures. Isolated suborders are a special kind of suborders and can be used to\ndiminish the number of elements of an ordered set by means of a quotient\nconstruction. The decisive point is that there are simple formulae establishing\nrelationships between the number of closures in the original ordered set and\nthe quotient thereof induced by isolated suborders. We show how these\nconnections can be used to derive a recursive algorithm for counting closures,\nprovided the ordered set under consideration contains suitable isolated\nsuborders.<\/jats:p>","DOI":"10.46298\/lmcs-20(3:11)2024","type":"journal-article","created":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T20:05:32Z","timestamp":1722888332000},"source":"Crossref","is-referenced-by-count":0,"title":["Isolated Suborders and their Application to Counting Closure Operators"],"prefix":"10.46298","volume":"Volume 20, Issue 3","author":[{"given":"Roland","family":"Gl\u00fcck","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,8,5]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/14028\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/14028\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T20:05:32Z","timestamp":1722888332000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,5]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(3:11)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2302.13081v5","asserted-by":"subject"},{"id-type":"arxiv","id":"2302.13081v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2302.13081v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2302.13081","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2302.13081","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,8,5]]},"article-number":"11009"}}