{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T13:17:41Z","timestamp":1773926261088,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2014,8,22]],"date-time":"2014-08-22T00:00:00Z","timestamp":1408665600000},"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":[[2014,12]]},"DOI":"10.1007\/s00493-014-2978-6","type":"journal-article","created":{"date-parts":[[2014,8,22]],"date-time":"2014-08-22T03:47:38Z","timestamp":1408679258000},"page":"689-706","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Three-point configurations determined by subsets of $$\\mathbb{F}_q^2$$ via the Elekes-Sharir Paradigm"],"prefix":"10.1007","volume":"34","author":[{"given":"Mike","family":"Bennett","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alex","family":"Iosevich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Pakianathan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,8,22]]},"reference":[{"issue":"3","key":"2978_CR1","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/BF02764959","volume":"54","author":"J. Bourgain","year":"1986","unstructured":"J. Bourgain: A Szemer\u00e9di type theorem for sets of positive density, Israel J. Math. 54 (1986), no. 3, 307\u2013331.","journal-title":"Israel J. Math."},{"key":"2978_CR2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s00039-004-0451-1","volume":"14","author":"J. Bourgain","year":"2004","unstructured":"J. Bourgain, N. Katz and T. Tao: A sum-product estimate in finite flelds, and applications, Geom. Func. Anal. 14 (2004), 27\u201357.","journal-title":"Geom. Func. Anal."},{"key":"2978_CR3","volume-title":"Research Problems in Discrete Geometry","author":"P. Brass","year":"2005","unstructured":"P. Brass, W. Moser and J. Pach: Research Problems in Discrete Geometry, Springer (2005)."},{"key":"2978_CR4","volume-title":"Math-ematische Zeitschrift","author":"J. Chapman","year":"2011","unstructured":"J. Chapman, B. Erdogan, D. Hart, A. Iosevich and D. Koh: Pinned distance sets, k-simplices, Wolff\u2019s exponent in finite flelds and sum-product estimates, Math-ematische Zeitschrift, (online; paper version to appear), (2011)."},{"key":"2978_CR5","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0012-365X(88)90049-0","volume":"69","author":"K. B. Chilakamarri","year":"1988","unstructured":"K. B. Chilakamarri: Unit-distance graphs in rational n-spaces, Discrete Math. 69 (1988), 213\u2013218.","journal-title":"Discrete Math."},{"key":"2978_CR6","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.disc.2010.10.009","volume":"311","author":"D. Covert","year":"2011","unstructured":"D. Covert, D. Hart, A. Iosevich, S. Senger and I. Uriarte-Tuero: An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density in finite fleld geometries, Discrete Math. 311 (2011), 423\u2013430.","journal-title":"Discrete Math."},{"key":"2978_CR7","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1017\/S0963548311000137","volume":"20","author":"G. Elekes","year":"2011","unstructured":"G. Elekes and M. Sharir: Incidences in three dimensions and distinct distances in the plane, Combin. Probab. Comput. 20 (2011), 571\u2013608.","journal-title":"Combin. Probab. Comput."},{"key":"2978_CR8","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s00454-004-1155-x","volume":"34","author":"C. Elsholtz","year":"2005","unstructured":"C. Elsholtz, W. Klotz: Maximal Dimension of Unit Simplices, Discrete and Computational Geometry, 34 (2005), 167\u2013177.","journal-title":"Discrete and Computational Geometry"},{"key":"2978_CR9","doi-asserted-by":"crossref","first-page":"248","DOI":"10.2307\/2305092","volume":"53","author":"P. Erd\u0151s","year":"1946","unstructured":"P. Erd\u0151s: On sets of distances of n points, Amer. Math. Monthly 53 (1946), 248\u2013250.","journal-title":"Amer. Math. Monthly"},{"key":"2978_CR10","doi-asserted-by":"crossref","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. Combin. Theory Ser. A 10 (1971), 246\u2013252.","journal-title":"J. Combin. Theory Ser."},{"key":"2978_CR11","first-page":"291","volume-title":"Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1975)","author":"P. Erd\u0151s","year":"1975","unstructured":"P. Erd\u0151s and G. Purdy: Some extremal problems in geometry III, Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1975), 291\u2013308, Congressus Numerantium, No. XIV, Utilitas Math., Winnipeg (1975)."},{"key":"2978_CR12","first-page":"307","volume-title":"Proceedings of the Seventh Southeastern Conference on Combinatorics, Graph Theory, and Computing (Louisiana State Univ., Baton Rouge, La., 1976)","author":"P. Erd\u0151s","year":"1976","unstructured":"P. Erd\u0151s and G. Purdy: Some extremal problems in geometry IV, Proceedings of the Seventh Southeastern Conference on Combinatorics, Graph Theory, and Computing (Louisiana State Univ., Baton Rouge, La., 1976), 307\u2013322, Congressus Numerantium, No. XVII, Utilitas Math., Winnipeg (1976)."},{"key":"2978_CR13","first-page":"569","volume-title":"Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977)","author":"P. Erd\u0151s","year":"1977","unstructured":"P. Erd\u0151s and G. Purdy: Some extremal problems in geometry V, Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), 569\u2013578, Congressus Numerantium, No. XIX, Utilitas Math., Winnipeg (1977)."},{"key":"2978_CR14","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0097-3165(78)90085-7","volume":"25","author":"P. Erd\u0151s","year":"1978","unstructured":"P. Erd\u0151s and G. Purdy: Some combinatorial problems in the plane, J. Combin. Theory Ser. A 25 (1978), 205\u2013210.","journal-title":"J. Combin. Theory Ser. A"},{"key":"2978_CR15","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, 2 vols, 809\u2013874, Elsevier Sci. B. V., Amsterdam (1995).","edition":"2"},{"key":"2978_CR16","volume-title":"The geometry of fractal sets","author":"K. J. Falconer","year":"1986","unstructured":"K. J. Falconer: The geometry of fractal sets, Cambridge Tracts in Mathematics, 85 Cambridge Univ. Pr., Cambridge (1986)."},{"key":"2978_CR17","first-page":"184","volume-title":"Ergodic theory and configurations in sets of positive density, Mathematics of Ramsey theory","author":"H. Furstenberg","year":"1990","unstructured":"H. Furstenberg, Y. Katznelson and B. Weiss: Ergodic theory and configurations in sets of positive density, Mathematics of Ramsey theory, 184\u2013198, Algorithms Combin., 5, Springer, Berlin (1990)."},{"key":"2978_CR18","volume-title":"Analysis and PDE","author":"A. Greeneleaf","year":"2010","unstructured":"A. Greeneleaf and A. Iosevich: On three point configurations determined by subsets of the Euclidean plane, the associated bilinear operator and applications to discrete geometry, Analysis and PDE (accepted for publication), (2010)."},{"key":"2978_CR19","unstructured":"L. Guth and N. Katz: On the Erd\u0151s distinct distance problem in the plane, (preprint) http:\/\/arxiv.org\/pdf\/1011.4105 ."},{"key":"2978_CR20","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1090\/S0002-9939-04-07603-8","volume":"133","author":"S. Hofmann","year":"2005","unstructured":"S. Hofmann and A. Iosevich: Circular averages and Falconer\/Erd\u0151s distance conjecture in the plane for random metrics, Proc. Amer. Math. Soc. 133 (2005), 133\u2013143.","journal-title":"Proc. Amer. Math. Soc."},{"key":"2978_CR21","doi-asserted-by":"crossref","first-page":"6595","DOI":"10.1090\/S0002-9947-09-04866-1","volume":"361","author":"A. Iosevich","year":"2009","unstructured":"A. Iosevich, H. Jorati and I. Laba: Geometric incidence theorems via Fourier analysis, Trans. Amer. Math. Soc. 361 (2009), 6595\u20136611.","journal-title":"Trans. Amer. Math. Soc."},{"key":"2978_CR22","first-page":"11","volume":"5","author":"A. Iosevich","year":"2005","unstructured":"A. Iosevich, I. Laba: K-distance sets, Falconer conjecture, and discrete analogues, Integers 5 (2005), 11.","journal-title":"Integers"},{"key":"2978_CR23","volume-title":"Erd\u0151s distance problem in vector spaces over finite flelds","author":"A. Iosevich","year":"2007","unstructured":"A. Iosevich and M. Rudnev: Erd\u0151s distance problem in vector spaces over finite flelds, Transactions of the American Mathematical Society, (2007)."},{"key":"2978_CR24","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511623813","volume-title":"Geometry of sets and measures in Euclidean spaces","author":"P. Mattila","year":"1995","unstructured":"P. Mattila: Geometry of sets and measures in Euclidean spaces, Cambridge Univ. Pr., 44 (1995).","edition":"44"},{"key":"2978_CR25","volume-title":"A course in the theory of groups","author":"D. Robinson","year":"1995","unstructured":"D. Robinson: A course in the theory of groups, Second Edition, Graduate Texts in Mathematics, Springer, 80, (1995).","edition":"Second"},{"key":"2978_CR26","first-page":"293","volume-title":"Graph theory and combinatorics","author":"J. Spencer","year":"1984","unstructured":"J. Spencer, E. Szemer\u00e9di and W. T. Trotter, Jr.: Unit distances in the Euclidean plane, Graph theory and combinatorics, 293\u2013303, Academic Press, London, (1984)."},{"key":"2978_CR27","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/BF02579194","volume":"3","author":"E. Szemer\u00e9di","year":"1983","unstructured":"E. Szemer\u00e9di and W. T. Trotter, Jr.: Extremal problems in discrete geometry, Combinatorica 3 (1983), 381\u2013392.","journal-title":"Combinatorica"},{"key":"2978_CR28","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1017\/S0963548397002976","volume":"6","author":"L. Sz\u00e9kely","year":"1997","unstructured":"L. Sz\u00e9kely: A. Crossing numbers and hard Erd\u0151s problems in discrete geometry Combin. Probab. Comput. 6 (1997), 353\u2013358.","journal-title":"Combin. Probab. Comput."},{"key":"2978_CR29","volume-title":"Szemeredi-Trotter type theorem and sum-product estimate in finite flelds","author":"L. Vinh","year":"2008","unstructured":"L. Vinh: Szemeredi-Trotter type theorem and sum-product estimate in finite flelds, (preprint), http:\/\/arxiv.org\/pdf\/0711.4427 (2008)."},{"key":"2978_CR30","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF02789447","volume":"99","author":"T. Ziegler","year":"2006","unstructured":"T. Ziegler: Nilfactors of \u211dd actions and configurations in sets of positive upper density in \u211dm, J. Anal. Math. 99 (2006), 249\u2013266.","journal-title":"J. Anal. Math."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-014-2978-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-014-2978-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-014-2978-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T21:32:50Z","timestamp":1559079170000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-014-2978-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,22]]},"references-count":30,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["2978"],"URL":"https:\/\/doi.org\/10.1007\/s00493-014-2978-6","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8,22]]}}}