{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T12:23:00Z","timestamp":1763727780701,"version":"build-2065373602"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,7,29]],"date-time":"2020-07-29T00:00:00Z","timestamp":1595980800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,29]],"date-time":"2020-07-29T00:00:00Z","timestamp":1595980800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1800746","NSF CAREER award"],"award-info":[{"award-number":["DMS-1800746","NSF CAREER award"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s00454-020-00231-x","type":"journal-article","created":{"date-parts":[[2020,7,29]],"date-time":"2020-07-29T14:02:31Z","timestamp":1596031351000},"page":"1232-1243","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On Grids in Point-Line Arrangements in the Plane"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7149-3592","authenticated-orcid":false,"given":"Mozhgan","family":"Mirzaei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew","family":"Suk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,29]]},"reference":[{"issue":"2","key":"231_CR1","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/BF01215345","volume":"14","author":"B Aronov","year":"1994","unstructured":"Aronov, B., Erd\u0151s, P., Goddard, W., Kleitman, D.J., Klugerman, M., Pach, J., Schulman, L.J.: Crossing families. Combinatorica 14(2), 127\u2013134 (1994)","journal-title":"Combinatorica"},{"key":"231_CR2","volume-title":"Research Problems in Discrete Geometry","author":"P Brass","year":"2005","unstructured":"Brass, P., Moser, W., Pach, J.: Research Problems in Discrete Geometry. Springer, New York (2005)"},{"issue":"3","key":"231_CR3","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1017\/S096354831100040X","volume":"21","author":"B Bukh","year":"2012","unstructured":"Bukh, B., Hubard, A.: Space crossing numbers. Comb. Probab. Comput. 21(3), 358\u2013373 (2012)","journal-title":"Comb. Probab. Comput."},{"issue":"4","key":"231_CR4","doi-asserted-by":"publisher","first-page":"#\u00a04.12","DOI":"10.37236\/3860","volume":"21","author":"J Cilleruelo","year":"2014","unstructured":"Cilleruelo, J., Timmons, C.: $$k$$-fold Sidon sets. Electron. J. Comb. 21(4), #\u00a04.12 (2014)","journal-title":"Electron. J. Comb."},{"key":"231_CR5","doi-asserted-by":"publisher","first-page":"161","DOI":"10.2307\/1969503","volume":"51","author":"RP Dilworth","year":"1950","unstructured":"Dilworth, R.P.: A decomposition theorem for partially ordered sets. Ann. Math. 51, 161\u2013166 (1950)","journal-title":"Ann. Math."},{"issue":"1","key":"231_CR6","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1007\/s00454-012-9464-y","volume":"49","author":"V Dujmovi\u0107","year":"2013","unstructured":"Dujmovi\u0107, V., Langerman, S.: A center transversal theorem for hyperplanes and applications to graph drawing. Discrete Comput. Geom. 49(1), 74\u201388 (2013)","journal-title":"Discrete Comput. Geom."},{"issue":"4","key":"231_CR7","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1112\/jlms\/s1-16.4.212","volume":"16","author":"P Erd\u00f6s","year":"1941","unstructured":"Erd\u00f6s, P., Tur\u00e1n, P.: On a problem of Sidon in additive number theory, and on some related problems. J. Lond. Math. Soc. 16(4), 212\u2013215 (1941)","journal-title":"J. Lond. Math. Soc."},{"key":"231_CR8","first-page":"49","volume":"671","author":"J Fox","year":"2012","unstructured":"Fox, J., Gromov, M., Lafforgue, V., Naor, A., Pach, J.: Overlap properties of geometric expanders. J. Reine Angew. Math. 671, 49\u201383 (2012)","journal-title":"J. Reine Angew. Math."},{"issue":"6","key":"231_CR9","doi-asserted-by":"publisher","first-page":"2199","DOI":"10.1137\/15M1007355","volume":"45","author":"J Fox","year":"2016","unstructured":"Fox, J., Pach, J., Suk, A.: A polynomial regularity lemma for semialgebraic hypergraphs and its applications in geometry and property testing. SIAM J. Comput. 45(6), 2199\u20132223 (2016)","journal-title":"SIAM J. Comput."},{"key":"231_CR10","doi-asserted-by":"publisher","first-page":"50","DOI":"10.4064\/cm-3-1-50-57","volume":"3","author":"T K\u00f6vari","year":"1954","unstructured":"K\u00f6vari, T., S\u00f3s, V.T., Tur\u00e1n, P.: On a problem of K. Zarankiewicz. Colloq. Math. 3, 50\u201357 (1954)","journal-title":"Zarankiewicz. Colloq. Math."},{"key":"231_CR11","doi-asserted-by":"publisher","first-page":"#\u00a025","DOI":"10.37236\/1718","volume":"10","author":"F Lazebnik","year":"2003","unstructured":"Lazebnik, F., Verstra\u00ebte, J.: On hypergraphs of girth five. Electron. J. Comb. 10, #\u00a025 (2003)","journal-title":"Electron. J. Comb."},{"issue":"3","key":"231_CR12","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/BF02293051","volume":"8","author":"J Matou\u0161ek","year":"1992","unstructured":"Matou\u0161ek, J.: Efficient partition trees. Discrete Comput. Geom. 8(3), 315\u2013334 (1992)","journal-title":"Discrete Comput. Geom."},{"key":"231_CR13","volume-title":"Combinatorial Geometry. Wiley-Interscience Series in Discrete Mathematics and Optimization","author":"J Pach","year":"1995","unstructured":"Pach, J., Agarwal, P.K.: Combinatorial Geometry. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York (1995)"},{"issue":"3","key":"231_CR14","doi-asserted-by":"publisher","first-page":"259","DOI":"10.4064\/aa-65-3-259-282","volume":"65","author":"IZ Ruzsa","year":"1993","unstructured":"Ruzsa, I.Z.: Solving a linear equation in a set of integers I. Acta Arithmetica 65(3), 259\u2013282 (1993)","journal-title":"Acta Arithmetica"},{"issue":"3","key":"231_CR15","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1137\/05062826X","volume":"20","author":"J Solymosi","year":"2006","unstructured":"Solymosi, J.: Dense arrangements are locally very dense. I. SIAM J. Discrete Math. 20(3), 623\u2013627 (2006)","journal-title":"SIAM J. Discrete Math."},{"key":"231_CR16","doi-asserted-by":"crossref","unstructured":"Suk, A., Tomon, I.: Hasse diagrams with large chromatic number (2020). arXiv:2001.09901","DOI":"10.1112\/blms.12457"},{"issue":"3\u20134","key":"231_CR17","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/BF02579194","volume":"3","author":"E Szemer\u00e9di","year":"1983","unstructured":"Szemer\u00e9di, E., Trotter Jr., W.T.: Extremal problems in discrete geometry. Combinatorica 3(3\u20134), 381\u2013392 (1983)","journal-title":"Combinatorica"},{"key":"231_CR18","doi-asserted-by":"crossref","unstructured":"Verstra\u00ebte, J.: Extremal problems for cycles in graphs. In: Recent Trends in Combinatorics. IMA Vol. Math. Appl., vol. 159, pp. 83\u2013116. Springer, Cham (2016)","DOI":"10.1007\/978-3-319-24298-9_4"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00231-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-020-00231-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00231-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,28]],"date-time":"2021-07-28T23:33:07Z","timestamp":1627515187000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-020-00231-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,29]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["231"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00231-x","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2020,7,29]]},"assertion":[{"value":"28 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}