{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:51:04Z","timestamp":1773147064376,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2012,5,1]],"date-time":"2012-05-01T00:00:00Z","timestamp":1335830400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2012,5]]},"DOI":"10.1007\/s00493-012-2505-6","type":"journal-article","created":{"date-parts":[[2012,10,4]],"date-time":"2012-10-04T03:03:47Z","timestamp":1349319827000},"page":"537-571","source":"Crossref","is-referenced-by-count":33,"title":["How to find groups? (and how to use them in Erd\u0151s geometry?)"],"prefix":"10.1007","volume":"32","author":[{"given":"Gy\u00f6rgy","family":"Elekes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Endre","family":"Szab\u00f3","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,10,4]]},"reference":[{"issue":"1\u20132","key":"2505_CR1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0925-7721(02)00127-X","volume":"25","author":"P. Brass","year":"2003","unstructured":"P. Brass and C. Knauer: On counting point-hyperplane incidences, Comput. Geom. Theory Appl. 25(1\u20132) (2003), 13\u201320.","journal-title":"Comput. Geom. Theory Appl."},{"key":"2505_CR2","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0304-3975(91)90261-Y","volume":"84","author":"B. Chazelle","year":"1991","unstructured":"B. Chazelle, H. Edelsbrunner, L. Guibas, and M. Sharir: A singly-exponential stratification scheme for real semi-algebraic varieties and its applications, Theoretical Computer Science 84 (1991), 77\u2013105.","journal-title":"Theoretical Computer Science"},{"key":"2505_CR3","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF01200753","volume":"15","author":"Gy. Elekes","year":"1995","unstructured":"Gy. Elekes: Circle grids and bipartite graphs of distances, Combinatorica 15 (1995), 167\u2013174.","journal-title":"Combinatorica"},{"key":"2505_CR4","doi-asserted-by":"crossref","first-page":"365","DOI":"10.4064\/aa-81-4-365-367","volume":"LXXXI.4","author":"Gy. Elekes","year":"1997","unstructured":"Gy. Elekes: On the number of sums and products, Acta Arithmetica LXXXI.4 (1997), 365\u2013367.","journal-title":"Acta Arithmetica"},{"key":"2505_CR5","first-page":"241","volume-title":"Paul Erd\u0151s and his mathematics, II (Budapest, 1999), Bolyai Soc. Math. Stud.","author":"Gy. Elekes","year":"2002","unstructured":"Gy. Elekes. Sums versus products in number theory, algebra and Erd\u0151s geometry, Paul Erd\u0151s and his mathematics, II (Budapest, 1999), Bolyai Soc. Math. Stud. 11, J\u00e1nos Bolyai Math. Soc., Budapest, 2002, 241\u2013290."},{"key":"2505_CR6","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/BF02187746","volume":"4","author":"P. Erd\u0151s","year":"1989","unstructured":"P. Erd\u0151s, L. Lov\u00e1sz, and K. Vesztergombi: On graphs of large distances, Discrete and Computational Geometry 4 (1989), 541\u2013549.","journal-title":"Discrete and Computational Geometry"},{"key":"2505_CR7","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1006\/jnth.1999.2386","volume":"83","author":"Gy. Elekes","year":"1999","unstructured":"Gy. Elekes, M. B. Nathanson, and I. Z. Ruzsa: Convexity and sumsets, Journal of Number Theory 83 (1999), 194\u2013201.","journal-title":"Journal of Number Theory"},{"key":"2505_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jcta.1999.2976","volume":"89","author":"Gy. Elekes","year":"2000","unstructured":"Gy. Elekes and L. R\u00f3nyai: A combinatorial problem on polynomials and rational functions, Journal of Combinatorial Theory, series A 89 (2000), 1\u201320.","journal-title":"Journal of Combinatorial Theory, series A"},{"key":"2505_CR9","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/BF02698687","volume":"53","author":"M. Gromov","year":"1981","unstructured":"M. Gromov: Groups of polynomial growth and expanding maps, Publ. Math., Inst. Hautes \u00c9tud. Sci. 53 (1981), 53\u201378.","journal-title":"Publ. Math., Inst. Hautes \u00c9tud. Sci."},{"key":"2505_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2189-8","volume-title":"Algebraic geometry: A first course","author":"J. Harris","year":"1992","unstructured":"J. Harris: Algebraic geometry: A first course, Springer-Verlag, New York, 1992."},{"key":"2505_CR11","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1090\/conm\/058.1\/860410","volume":"58","author":"F. Hirzebruch","year":"1986","unstructured":"F. Hirzebruch: Singularities of algebraic surfaces and characteristic numbers, Contemp. Math. 58 (1986), 141\u2013155.","journal-title":"Contemp. Math."},{"key":"2505_CR12","volume-title":"PhD thesis","author":"E. Hrushovski","year":"1986","unstructured":"E. Hrushovski: Contributions to stable model theory, PhD thesis, University of California, Berkeley, 1986."},{"key":"2505_CR13","doi-asserted-by":"crossref","unstructured":"N. Jacobson: Lectures in abstract algebra, III. Theory of fields and Galois theory, University Series in Higher Mathematics, Van Nostrand Reinhold Co., 1964.","DOI":"10.1007\/978-1-4612-9872-4"},{"key":"2505_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03276-3","volume-title":"Rational Curves on Algebraic Varieties","author":"J. Koll\u00e1r","year":"1996","unstructured":"J. Koll\u00e1r: Rational Curves on Algebraic Varieties, Springer, Berlin, 1996."},{"key":"2505_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0039-7","volume-title":"Lectures on Discrete Geometry","author":"J. Matou\u0161ek","year":"2002","unstructured":"J. Matou\u0161ek: Lectures on Discrete Geometry, Springer-Verlag, Berlin, Heidelberg, New York, 2002."},{"key":"2505_CR16","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1007\/BF01444245","volume":"305","author":"G. Megyesi","year":"1996","unstructured":"G. Megyesi and E. Szab\u00f3: On the tacnodes of configurations of conics in the projective plane, Mathematische Annalen 305 (1996), 693\u2013703.","journal-title":"Mathematische Annalen"},{"key":"2505_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-74334-4","volume-title":"Lie groups and algebraic groups","author":"A. L. Onishchik","year":"1990","unstructured":"A. L. Onishchik and E. B. Vinberg: Lie groups and algebraic groups, Springer, Berlin, 1990."},{"key":"2505_CR18","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534372.001.0001","volume-title":"Geometric Stability Theory","author":"A. Pillay","year":"1996","unstructured":"A. Pillay: Geometric Stability Theory, volume 32 of Oxford Logic Guides, Clarendon Press, Oxford, 1996."},{"key":"2505_CR19","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1017\/S0963548397003192","volume":"7","author":"J. Pach","year":"1998","unstructured":"J. Pach and M. Sharir: On the number of incidences between points and curves, Combinatorics, Probability and Computing 7 (1998), 121\u2013127.","journal-title":"Combinatorics, Probability and Computing"},{"issue":"3\u20134","key":"2505_CR20","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(3\u20134) (1983), 381\u2013392.","journal-title":"Combinatorica"},{"key":"2505_CR21","doi-asserted-by":"crossref","first-page":"493","DOI":"10.2307\/2372637","volume":"77","author":"A. Weil","year":"1955","unstructured":"A. Weil: On algebraic groups and homogeneous spaces, American Journal of Mathematics 77 (1955), 493\u2013512.","journal-title":"American Journal of Mathematics"},{"key":"2505_CR22","doi-asserted-by":"crossref","first-page":"355","DOI":"10.2307\/2372535","volume":"77","author":"A. Weil","year":"1955","unstructured":"A. Weil: On algebraic groups of transformations, American Journal of Mathematics 77 (1955), 355\u2013391.","journal-title":"American Journal of Mathematics"}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-012-2505-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-012-2505-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-012-2505-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T00:28:13Z","timestamp":1714436893000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-012-2505-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5]]},"references-count":22,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2012,5]]}},"alternative-id":["2505"],"URL":"https:\/\/doi.org\/10.1007\/s00493-012-2505-6","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5]]}}}