{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T14:30:11Z","timestamp":1767018611457,"version":"3.48.0"},"reference-count":10,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T00:00:00Z","timestamp":1721779200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T00:00:00Z","timestamp":1721779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The lattice of noncrossing partitions is well-known for its wide variety of combinatorial appearances and properties. For example, the lattice is rank-symmetric and enumerated by the Catalan numbers. In this article, we introduce a large family of new noncrossing partition lattices with both of these properties, each parametrized by a configuration of\n                    <jats:italic>n<\/jats:italic>\n                    points in the plane.\n                  <\/jats:p>","DOI":"10.1007\/s00454-024-00682-6","type":"journal-article","created":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T13:01:45Z","timestamp":1721826105000},"page":"111-140","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Noncrossing Partition Lattices from Planar Configurations"],"prefix":"10.1007","volume":"75","author":[{"given":"Stella","family":"Cohen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5231-2730","authenticated-orcid":false,"given":"Michael","family":"Dougherty","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew D.","family":"Harsh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Spencer Park","family":"Martin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,24]]},"reference":[{"key":"682_CR1","doi-asserted-by":"crossref","unstructured":"Baumeister, B., Bux, K.-U., G\u00f6tze, F., Kielak, D., Krause, H.: Non-crossing partitions. 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Algebraic Combin."},{"issue":"7","key":"682_CR6","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1016\/j.comgeo.2011.07.001","volume":"46","author":"A Razen","year":"2013","unstructured":"Razen, A., Welzl, E.: On the number of crossing-free partitions. Comput. Geom. 46(7), 879\u2013893 (2013)","journal-title":"Comput. Geom."},{"issue":"3","key":"682_CR7","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1137\/050636036","volume":"36","author":"M Sharir","year":"2006","unstructured":"Sharir, M., Welzl, E.: On the number of crossing-free matchings, cycles, and partitions. SIAM J. Comput. 36(3), 695\u2013720 (2006)","journal-title":"SIAM J. Comput."},{"issue":"3","key":"682_CR8","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/0012-365X(91)90376-D","volume":"98","author":"R Simion","year":"1991","unstructured":"Simion, R., Ullman, D.: On the structure of the lattice of noncrossing partitions. Discrete Math. 98(3), 193\u2013206 (1991)","journal-title":"Discrete Math."},{"key":"682_CR9","unstructured":"Stanley, R.P.: Enumerative Combinatorics, vol. 1, 2nd edn. Cambridge Studies in Advanced Mathematics, vol.\u00a049, Cambridge University Press, Cambridge (2012)"},{"key":"682_CR10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139871495","volume-title":"Catalan Numbers","author":"RP Stanley","year":"2015","unstructured":"Stanley, R.P.: Catalan Numbers. Cambridge University Press, New York (2015)"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-024-00682-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-024-00682-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-024-00682-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T14:26:47Z","timestamp":1767018407000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-024-00682-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,24]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["682"],"URL":"https:\/\/doi.org\/10.1007\/s00454-024-00682-6","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2024,7,24]]},"assertion":[{"value":"20 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 July 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 July 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}