{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:29:46Z","timestamp":1760441386111},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2016,11,28]],"date-time":"2016-11-28T00:00:00Z","timestamp":1480291200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s00493-016-3440-8","type":"journal-article","created":{"date-parts":[[2016,11,28]],"date-time":"2016-11-28T07:26:20Z","timestamp":1480317980000},"page":"1221-1240","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Number of Unit-Area Triangles in the Plane: Theme and Variation"],"prefix":"10.1007","volume":"37","author":[{"given":"Orit E.","family":"Raz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Micha","family":"Sharir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,11,28]]},"reference":[{"key":"3440_CR1","volume-title":"Geometric Incidences and Repeated Configurations","author":"R. Apfelbaum","year":"2013","unstructured":"R. Apfelbaum: Geometric Incidences and Repeated Configurations, Ph.D. Dissertation, School of Computer Science, Tel Aviv University, 2013."},{"key":"3440_CR2","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1007\/s00454-010-9265-0","volume":"44","author":"R. Apfelbaum","year":"2010","unstructured":"R. Apfelbaum and M. Sharir: An improved bound on the number of unit-area triangles, Discrete Comput. Geom.\n                           44 (2010), 753\u2013761.","journal-title":"Discrete Comput. Geom."},{"key":"3440_CR3","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1016\/j.jcta.2009.03.008","volume":"116","author":"A. Dumitrescu","year":"2009","unstructured":"A. Dumitrescu, M. Sharir and Cs. D. T\u00f3th: Extremal problems on triangle areas in two and three dimensions, J. Combinat. Theory, Ser. A\n                           116 (2009), 1177\u20131198.","journal-title":"J. Combinat. Theory, Ser. A"},{"key":"3440_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jcta.1999.2976","volume":"89","author":"G. Elekes","year":"2000","unstructured":"G. Elekes and L. R\u00f3nyai: A combinatorial problem on polynomials and rational functions, J. Combinat. Theory Ser. A\n                           89 (2000), 1\u201320.","journal-title":"J. Combinat. Theory Ser. A"},{"key":"3440_CR5","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1007\/s00493-012-2505-6","volume":"32","author":"G. Elekes","year":"2012","unstructured":"G. Elekes and E. Szab\u00f3: How to find groups? (And how to use them in Erd\u0151s geometry?), Combinatorica\n                           32 (2012), 537\u2013571.","journal-title":"Combinatorica"},{"key":"3440_CR6","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/0097-3165(71)90028-8","volume":"10","author":"P. Erd\u0151s","year":"1971","unstructured":"P. Erd\u0151s and G. Purdy: Some extremal problems in geometry, J. Combinat. Theory\n                           10 (1971), 246\u2013252.","journal-title":"J. Combinat. Theory"},{"key":"3440_CR7","first-page":"809","volume-title":"Handbook of Combinatorics","author":"P. Erd\u0151s","year":"1995","unstructured":"P. Erd\u0151s and G. Purdy: Extremal problems in combinatorial geometry, in: Handbook of Combinatorics (R. Graham, M. Gr\u00f6tschel and L. Lov\u00e1sz, editors), Vol. 1, 809\u2013874, Elsevier, Amsterdam, 1995."},{"key":"3440_CR8","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/0097-3165(92)90094-B","volume":"59","author":"J. Pach","year":"1992","unstructured":"J. Pach and M. Sharir: Repeated angles in the plane and related problems, J. Combinat. Theory Ser. A\n                           59 (1992), 12\u201322.","journal-title":"J. Combinat. Theory Ser. A"},{"key":"3440_CR9","first-page":"569","volume-title":"Proc. 31st Annu. Sympos. Comput. Geom.","author":"O. E. Raz","year":"2015","unstructured":"O. E. Raz and M. Sharir: The number of unit-area triangles in the plane: Theme and variations, Proc. 31st Annu. Sympos. Comput. Geom., 2015, 569\u2013583. Also in arXiv:1501.00379."},{"key":"3440_CR10","unstructured":"O. E. Raz, M. Sharir and I. Shkredov: On the number of unit-area triangles spanned by convex grids in the plane, in arXiv:1504.06989."},{"key":"3440_CR11","doi-asserted-by":"publisher","first-page":"1029","DOI":"10.1353\/ajm.2016.0033","volume":"138","author":"O. E. Raz","year":"2016","unstructured":"O. E. Raz, M. Sharir and J. Solymosi: Polynomials vanishing on grids: The Elekes-R\u00f3nyai problem revisited, Amer. J. Math.\n                           138 (2016), 1029\u20131065. Also in Proc. 30th Annu. Sympos. Comput. Geom., 2014, 251-260.","journal-title":"Amer. J. Math."},{"key":"3440_CR12","unstructured":"O. E. Raz, M. Sharir and F. de Zeeuw: Polynomials vanishing on Cartesian products: The Elekes-Szab\u00f3 Theorem revisited, Duke Math. J., to appear. Also in arXiv:1504.05012."},{"key":"3440_CR13","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s00454-012-9420-x","volume":"48","author":"J. Solymosi","year":"2012","unstructured":"J. Solymosi and T. Tao: An incidence theorem in higher dimensions, Discrete Comput. Geom.\n                           48 (2012), 255\u2013280.","journal-title":"Discrete Comput. Geom."},{"key":"3440_CR14","unstructured":"J. Solymosi and F. de Zeeuw: Incidence bounds for complex algebraic curves on Cartesian products, arXiv:1502.05304v2."},{"key":"3440_CR15","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/BF02579194","volume":"3","author":"E. Szemer\u00e9di","year":"1983","unstructured":"E. Szemer\u00e9di and W. T. Trotter: Extremal problems in discrete geometry, Combinatorica\n                           3 (1983), 381\u2013392.","journal-title":"Combinatorica"},{"key":"3440_CR16","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/s00454-015-9717-7","volume":"54","author":"J. Zahl","year":"2015","unstructured":"J. Zahl: A Szemer\u00e9di-Trotter type theorem in R4, Discrete. Comput. Geom.\n                           54 (2015), 513\u2013572.","journal-title":"Discrete. Comput. Geom."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-016-3440-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-016-3440-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-016-3440-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,12,14]],"date-time":"2018-12-14T06:04:45Z","timestamp":1544767485000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-016-3440-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,28]]},"references-count":16,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["3440"],"URL":"https:\/\/doi.org\/10.1007\/s00493-016-3440-8","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,28]]}}}