{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T03:01:01Z","timestamp":1765422061758,"version":"3.37.3"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,2,9]],"date-time":"2018-02-09T00:00:00Z","timestamp":1518134400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Grantov\u00e1 Agentura Cesk\u00e9 Republiky","award":["14-14179S"],"award-info":[{"award-number":["14-14179S"]}]},{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura Cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["14-14179S"],"award-info":[{"award-number":["14-14179S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["267165","267165"],"award-info":[{"award-number":["267165","267165"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007543","name":"Grantov\u00e1 Agentura, Univerzita Karlova","doi-asserted-by":"publisher","award":["690214","690214"],"award-info":[{"award-number":["690214","690214"]}],"id":[{"id":"10.13039\/100007543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007543","name":"Grantov\u00e1 Agentura, Univerzita Karlova","doi-asserted-by":"publisher","award":["SVV-2016-260332"],"award-info":[{"award-number":["SVV-2016-260332"]}],"id":[{"id":"10.13039\/100007543","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":[[2019,3]]},"DOI":"10.1007\/s00454-018-9970-7","type":"journal-article","created":{"date-parts":[[2018,2,9]],"date-time":"2018-02-09T14:45:23Z","timestamp":1518187523000},"page":"325-354","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Covering Lattice Points by Subspaces and Counting Point\u2013Hyperplane Incidences"],"prefix":"10.1007","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9688-9489","authenticated-orcid":false,"given":"Martin","family":"Balko","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7844-6692","authenticated-orcid":false,"given":"Josef","family":"Cibulka","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3102-4166","authenticated-orcid":false,"given":"Pavel","family":"Valtr","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,2,9]]},"reference":[{"key":"9970_CR1","unstructured":"Ackerman, E.: On topological graphs with at most four crossings per edge. Submitted, preliminary version (2015) arxiv:1509.01932"},{"issue":"3","key":"9970_CR2","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1137\/050641375","volume":"21","author":"R Apfelbaum","year":"2007","unstructured":"Apfelbaum, R., Sharir, M.: Large complete bipartite subgraphs in incidence graphs of points and hyperplanes. SIAM J. Discrete Math. 21(3), 707\u2013725 (2007)","journal-title":"SIAM J. Discrete Math."},{"issue":"4","key":"9970_CR3","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1007\/BF01445125","volume":"296","author":"W Banaszczyk","year":"1993","unstructured":"Banaszczyk, W.: New bounds in some transference theorems in the geometry of numbers. Math. Ann. 296(4), 625\u2013635 (1993)","journal-title":"Math. Ann."},{"issue":"1\u20132","key":"9970_CR4","first-page":"93","volume":"43","author":"I B\u00e1r\u00e1ny","year":"2001","unstructured":"B\u00e1r\u00e1ny, I., Harcos, G., Pach, J., Tardos, G.: Covering lattice points by subspaces. Period. Math. Hung. 43(1\u20132), 93\u2013103 (2001)","journal-title":"Period. Math. Hung."},{"issue":"1\u20132","key":"9970_CR5","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/S0925-7721(02)00127-X","volume":"25","author":"P Brass","year":"2003","unstructured":"Brass, P., Knauer, C.: On counting point\u2013hyperplane incidences. Comput. Geom. 25(1\u20132), 13\u201320 (2003)","journal-title":"Comput. Geom."},{"key":"9970_CR6","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":"2","key":"9970_CR7","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/BF02189314","volume":"9","author":"B Chazelle","year":"1993","unstructured":"Chazelle, B.: Cutting hyperplanes for divide-and-conquer. Discrete Comput. Geom. 9(2), 145\u2013158 (1993)","journal-title":"Discrete Comput. Geom."},{"issue":"5","key":"9970_CR8","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1080\/00029890.1946.11991674","volume":"53","author":"P Erd\u0151s","year":"1946","unstructured":"Erd\u0151s, P.: On sets of distances of $$n$$ n points. Am. Math. Mon. 53(5), 248\u2013250 (1946)","journal-title":"Am. Math. Mon."},{"issue":"4","key":"9970_CR9","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/BF02712875","volume":"16","author":"J Erickson","year":"1996","unstructured":"Erickson, J.: New lower bounds for Hopcroft\u2019s problem. Discrete Comput. Geom. 16(4), 389\u2013418 (1996)","journal-title":"Discrete Comput. Geom."},{"issue":"6","key":"9970_CR10","doi-asserted-by":"publisher","first-page":"1785","DOI":"10.4171\/JEMS\/705","volume":"19","author":"J Fox","year":"2017","unstructured":"Fox, J., Pach, J., Sheffer, A., Suk, A., Zahl, J.: A semi-algebraic version of Zarankiewicz\u2019s problem. J. Eur. Math. Soc. (JEMS) 19(6), 1785\u20131810 (2017)","journal-title":"J. Eur. Math. Soc. (JEMS)"},{"issue":"6","key":"9970_CR11","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/0020-0190(90)90214-I","volume":"33","author":"T Hagerup","year":"1990","unstructured":"Hagerup, T., R\u00fcb, C.: A guided tour of Chernoff bounds. Inf. Process. Lett. 33(6), 305\u2013308 (1990)","journal-title":"Inf. Process. Lett."},{"issue":"I","key":"9970_CR12","first-page":"377","volume":"70","author":"M Henk","year":"2002","unstructured":"Henk, M.: Successive minima and lattice points. Rend. Circ. Mat. Palermo (2) Suppl 70(I), 377\u2013384 (2002)","journal-title":"Rend. Circ. Mat. Palermo (2) Suppl"},{"key":"9970_CR13","unstructured":"John, F.: Extremum problems with inequalities as subsidiary conditions. In: Studies and Essays. Presented to R. Courant on his 60th Birthday, January 8, 1948, pp. 187\u2013204. Interscience, New York (1948)"},{"key":"9970_CR14","unstructured":"Lefmann, H.: Extensions of the No-Three-In-Line problem. Submitted, preliminary version (2012). www.tu-chemnitz.de\/informatik\/ThIS\/downloads\/publications\/lefmann_no_three_submitted.pdf"},{"key":"9970_CR15","doi-asserted-by":"crossref","first-page":"93","DOI":"10.21136\/CPMF.1939.109441","volume":"68","author":"K Mahler","year":"1939","unstructured":"Mahler, K.: Ein \u00dcbertragungsprinzip f\u00fcr konvexe K\u00f6rper. \u010cas. Mat. Fys. 68, 93\u2013102 (1939)","journal-title":"\u010cas. Mat. Fys."},{"key":"9970_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0039-7","volume-title":"Lectures on Discrete Geometry. Graduate Texts in Mathematics","author":"J Matou\u0161ek","year":"2002","unstructured":"Matou\u0161ek, J.: Lectures on Discrete Geometry. Graduate Texts in Mathematics, vol. 212. Springer, New York (2002)"},{"key":"9970_CR17","volume-title":"Geometrie der Zahlen","author":"H Minkowski","year":"1910","unstructured":"Minkowski, H.: Geometrie der Zahlen. Teubner, Leipzig (1910)"},{"issue":"3","key":"9970_CR18","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/BF01215922","volume":"17","author":"J Pach","year":"1997","unstructured":"Pach, J., T\u00f3th, G.: Graphs drawn with few crossings per edge. Combinatorica 17(3), 427\u2013439 (1997)","journal-title":"Combinatorica"},{"key":"9970_CR19","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1112\/jlms\/s1-26.3.198","volume":"26","author":"KF Roth","year":"1951","unstructured":"Roth, K.F.: On a problem of Heilbronn. J. Lond. Math. Soc. 26, 198\u2013204 (1951)","journal-title":"J. Lond. Math. Soc."},{"key":"9970_CR20","doi-asserted-by":"crossref","unstructured":"Sheffer, A.: Lower bounds for incidences with hypersurfaces. Discrete Anal. 2016, Paper No. 16 (2016)","DOI":"10.19086\/da912"},{"key":"9970_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-08287-4","volume-title":"Lectures on the Geometry of Numbers","author":"CL Siegel","year":"1989","unstructured":"Siegel, C.L., Chandrasekharan, K.: Lectures on the Geometry of Numbers. Springer, Berlin (1989)"},{"issue":"3\u20134","key":"9970_CR22","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"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-018-9970-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-018-9970-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-018-9970-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T00:44:53Z","timestamp":1603845893000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-018-9970-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,9]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["9970"],"URL":"https:\/\/doi.org\/10.1007\/s00454-018-9970-7","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2018,2,9]]},"assertion":[{"value":"23 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 December 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 January 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}