{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:41:02Z","timestamp":1753890062208,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Permutation Patterns","license":[{"start":{"date-parts":[[2017,12,5]],"date-time":"2017-12-05T00:00:00Z","timestamp":1512432000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,12,5]],"date-time":"2017-12-05T00:00:00Z","timestamp":1512432000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,12,5]],"date-time":"2017-12-05T00:00:00Z","timestamp":1512432000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>A permutation class $C$ is splittable if it is contained in a merge of two of its proper subclasses, and it is 1-amalgamable if given two permutations $\\sigma$ and $\\tau$ in $C$, each with a marked element, we can find a permutation $\\pi$ in $C$ containing both $\\sigma$ and $\\tau$ such that the two marked elements coincide. It was previously shown that unsplittability implies 1-amalgamability. We prove that unsplittability and 1-amalgamability are not equivalent properties of permutation classes by showing that the class $Av(1423, 1342)$ is both splittable and 1-amalgamable. Our construction is based on the concept of LR-inflations, which we introduce here and which may be of independent interest.<\/jats:p><jats:p>Comment: 17 pages, 7 figures<\/jats:p>","DOI":"10.23638\/dmtcs-19-2-4","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:44:27Z","timestamp":1743698667000},"source":"Crossref","is-referenced-by-count":0,"title":["Splittability and 1-amalgamability of permutation classes"],"prefix":"10.23638","volume":"Vol. 19 no. 2, Permutation...","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4831-4079","authenticated-orcid":false,"given":"V\u00edt","family":"Jel\u00ednek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"Opler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2017,12,5]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1704.08732v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1704.08732v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:44:27Z","timestamp":1743698667000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/3292"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,5]]},"references-count":0,"journal-issue":{"issue":"Permutation Patterns","published-online":{"date-parts":[[2017,12,5]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-19-2-4","relation":{"has-preprint":[{"id-type":"arxiv","id":"1704.08732v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1704.08732v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1704.08732","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1704.08732","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2017,12,5]]},"article-number":"3292"}}