{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T00:26:55Z","timestamp":1648945615061},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,6,27]],"date-time":"2015-06-27T00:00:00Z","timestamp":1435363200000},"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":[[2016,4]]},"DOI":"10.1007\/s00493-015-3100-4","type":"journal-article","created":{"date-parts":[[2015,6,29]],"date-time":"2015-06-29T04:15:57Z","timestamp":1435551357000},"page":"229-248","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Maximal sets with no solution to x+y=3z"],"prefix":"10.1007","volume":"36","author":[{"given":"Alain","family":"Plagne","sequence":"first","affiliation":[]},{"given":"Anne","family":"de Roton","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,6,27]]},"reference":[{"key":"3100_CR1","doi-asserted-by":"crossref","unstructured":"A. Baltz, P. Hegarty, J. Knape, U. Larsson and T. Schoen: The structure of maximum subsets of {1,\u2026, n} with no solutions to a+b=kc, Electron. J. Combin. 12 (2005), Research Paper 19.","DOI":"10.37236\/1916"},{"key":"3100_CR2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10474-011-0124-0","volume":"132","author":"P. Candela","year":"2011","unstructured":"P. Candela and O. Sisask: On the asymptotic maximal density of a set avoiding solutions to linear equations modulo a prime, Acta Math. Hungar. 132 (2011), 223\u2013243.","journal-title":"Hungar"},{"key":"3100_CR3","doi-asserted-by":"crossref","unstructured":"F. R. K. Chung and J. L. Goldwasser: Maximum subsets of [0; 1] with no solutions to x+y=kz, Electron. J. Combin. 3 (1996).","DOI":"10.37236\/1225"},{"key":"3100_CR4","unstructured":"F. R. K. Chung and J. L. Goldwasser: Integer Sets Containing no Solution to x+y=3z, The mathematics of Paul Erd\u0151s (1997), Springer, 218-227."},{"key":"3100_CR5","first-page":"149","volume":"258","author":"J.-M. Deshouillers","year":"1999","unstructured":"J.-M. Deshouillers, G. A. Freiman, V. S\u00f3s and M. Temkin: On the structure of sum-free sets, 2, Ast\u00e9risque 258 (1999), 149\u2013161.","journal-title":"Ast\u00e9risque"},{"key":"3100_CR6","doi-asserted-by":"crossref","first-page":"313","DOI":"10.4064\/aa121-4-2","volume":"121","author":"K. Dilcher","year":"2006","unstructured":"K. Dilcher and L. Lucht: Onnite pattern-free sets of integers, Acta Arith. 121 (2006), 313\u2013325.","journal-title":"Acta Arith"},{"key":"3100_CR7","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1112\/plms\/s3-3.1.182","volume":"3","author":"R. Henstock","year":"1953","unstructured":"R. Henstock and A. M. Macbeath: On the measure of sum sets, I. The theorems of Brunn, Minkowski and Lusternik, Proc. London Math. Soc. 3 (1953), 182\u2013194.","journal-title":"Proc. London Math. Soc"},{"key":"3100_CR8","first-page":"209","volume":"285","author":"L. Lucht","year":"1976","unstructured":"L. Lucht: Dichteschranken f\u00fcr die L\u00f6sbarkeit gewisser linearer Gleichungen, J. Reine Angew. Math. 285 (1976), 209\u2013217.","journal-title":"J. Reine Angew. Math"},{"key":"3100_CR9","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1016\/j.ejc.2013.05.024","volume":"34","author":"M. Matolcsi","year":"2013","unstructured":"M. Matolcsi and I. Z. Ruzsa: Sets with no solutions to x+y=3z, Europ. J. Combin. 34 (2013), 1411\u20131414.","journal-title":"Europ. J. Combin"},{"key":"3100_CR10","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1112\/jlms\/s1-28.1.104","volume":"28","author":"K. F. Roth","year":"1953","unstructured":"K. F. Roth: On certain sets of integers, J. London Math. Soc. 28 (1953), 104\u2013109.","journal-title":"J. London Math. Soc"},{"key":"3100_CR11","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/BF01351772","volume":"112","author":"I. Z. Ruzsa","year":"1991","unstructured":"I. Z. Ruzsa: Diameter of sets and measure of sumsets, Monatsh. Math. 112 (1991),323\u2013328.","journal-title":"Monatsh. Math"},{"key":"3100_CR12","doi-asserted-by":"crossref","first-page":"259","DOI":"10.4064\/aa-65-3-259-282","volume":"65","author":"I. Z. Ruzsa","year":"1993","unstructured":"I. Z. Ruzsa: Solving a linear equation in a set of integers I, Acta Arith. 65 (1993), 259\u2013282.","journal-title":"Acta Arith"},{"key":"3100_CR13","doi-asserted-by":"crossref","first-page":"385","DOI":"10.4064\/aa-72-4-385-397","volume":"72","author":"I. Z. Ruzsa","year":"1995","unstructured":"I. Z. Ruzsa: Solving a linear equation in a set of integers II, Acta Arith. 72 (1995), 385\u2013397.","journal-title":"Acta Arith"},{"key":"3100_CR14","doi-asserted-by":"crossref","first-page":"619","DOI":"10.4007\/annals.2011.174.1.20","volume":"174","author":"T. Sanders","year":"2011","unstructured":"T. Sanders: On Roth\u2019s theorem on progressions, Ann. of Math. 174 (2011), 619\u2013636.","journal-title":"Ann. of Math"},{"key":"3100_CR15","first-page":"114","volume":"25","author":"I. Schur","year":"1917","unstructured":"I. Schur: \u00dcber die Kongruenz x m +y m = z m (mod p), Jahresber. Deutsch. Math.-Verein. 25 (1917), 114\u2013117.","journal-title":"Jahresber. Deutsch. Math.-Verein"},{"key":"3100_CR16","doi-asserted-by":"crossref","first-page":"105","DOI":"10.4064\/fm-1-1-105-111","volume":"1","author":"W. Sierpi\u0144ski","year":"1920","unstructured":"W. Sierpi\u0144ski: Surla question de la mesurabilit\u00e9 de la base de M. Hamel, Fund. Math 1 (1920), 105\u2013111.","journal-title":"Fund. Math"},{"key":"3100_CR17","doi-asserted-by":"crossref","unstructured":"W. D. Wallis, A. P. Street and J. S. Wallis: Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices, Lecture Notes in Mathematics 292, Springer, 1972.","DOI":"10.1007\/BFb0069907"}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-015-3100-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-015-3100-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-015-3100-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T05:25:29Z","timestamp":1599197129000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-015-3100-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,27]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,4]]}},"alternative-id":["3100"],"URL":"https:\/\/doi.org\/10.1007\/s00493-015-3100-4","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,27]]}}}