{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:01Z","timestamp":1740109561770,"version":"3.37.3"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T00:00:00Z","timestamp":1567036800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T00:00:00Z","timestamp":1567036800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100011019","name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","doi-asserted-by":"publisher","award":["116451","121649"],"award-info":[{"award-number":["116451","121649"]}],"id":[{"id":"10.13039\/501100011019","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011019","name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","doi-asserted-by":"publisher","award":["129630","109789"],"award-info":[{"award-number":["129630","109789"]}],"id":[{"id":"10.13039\/501100011019","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010789","name":"Direcci\u00f3n General de Universidades e Investigaci\u00f3n","doi-asserted-by":"publisher","award":["MTM2017-83750-P","MTM2017-82166-P"],"award-info":[{"award-number":["MTM2017-83750-P","MTM2017-82166-P"]}],"id":[{"id":"10.13039\/501100010789","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010789","name":"Direcci\u00f3n General de Universidades e Investigaci\u00f3n","doi-asserted-by":"publisher","award":["MDM-2014-0445"],"award-info":[{"award-number":["MDM-2014-0445"]}],"id":[{"id":"10.13039\/501100010789","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006188","name":"Einstein Stiftung Berlin","doi-asserted-by":"publisher","award":["EVF-2015-230"],"award-info":[{"award-number":["EVF-2015-230"]}],"id":[{"id":"10.13039\/501100006188","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":[[2020,9]]},"DOI":"10.1007\/s00454-019-00131-9","type":"journal-article","created":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T12:15:18Z","timestamp":1567080918000},"page":"396-426","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Triangulations and a Discrete Brunn\u2013Minkowski Inequality in the Plane"],"prefix":"10.1007","volume":"64","author":[{"given":"K\u00e1roly J.","family":"B\u00f6r\u00f6czky","sequence":"first","affiliation":[]},{"given":"M\u00e1t\u00e9","family":"Matolcsi","sequence":"additional","affiliation":[]},{"given":"Imre Z.","family":"Ruzsa","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2120-9068","authenticated-orcid":false,"given":"Francisco","family":"Santos","sequence":"additional","affiliation":[]},{"given":"Oriol","family":"Serra","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,29]]},"reference":[{"issue":"1","key":"131_CR1","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/0097-3165(91)90021-8","volume":"56","author":"B Bollob\u00e1s","year":"1991","unstructured":"Bollob\u00e1s, B., Leader, I.: Compressions and isoperimetric inequalities. J. Combin. Theory A 56(1), 47\u201362 (1991)","journal-title":"J. Combin. Theory A"},{"issue":"1","key":"131_CR2","doi-asserted-by":"publisher","first-page":"75","DOI":"10.2140\/involve.2015.8.75","volume":"8","author":"KJ B\u00f6r\u00f6czky","year":"2015","unstructured":"B\u00f6r\u00f6czky, K.J., Hoffman, B.: A note on triangulations of sumsets. Involve 8(1), 75\u201385 (2015)","journal-title":"Involve"},{"key":"131_CR3","volume-title":"Triangulations. Algorithms and Computation in Mathematics","author":"JA De Loera","year":"2010","unstructured":"De Loera, J.A., Rambau, J., Santos, F.: Triangulations. Algorithms and Computation in Mathematics, vol. 25. Springer, Berlin (2010)"},{"key":"131_CR4","volume-title":"Foundations of a Structural Theory of Set Addition. Translations of Mathematical Monographs","author":"GA Freiman","year":"1973","unstructured":"Freiman, G.A.: Foundations of a Structural Theory of Set Addition. Translations of Mathematical Monographs, vol. 37. American Mathematical Society, Providence (1973)"},{"issue":"10","key":"131_CR5","doi-asserted-by":"publisher","first-page":"3995","DOI":"10.1090\/S0002-9947-01-02763-5","volume":"353","author":"RJ Gardner","year":"2001","unstructured":"Gardner, R.J., Gronchi, P.: A Brunn\u2013Minkowski inequality for the integer lattice. Trans. Am. Math. Soc. 353(10), 3995\u20134024 (2001)","journal-title":"Trans. Am. Math. Soc."},{"issue":"4","key":"131_CR6","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1093\/qmath\/hal009","volume":"57","author":"B Green","year":"2006","unstructured":"Green, B., Tao, T.: Compressions, convex geometry and the Freiman\u2013Bilu theorem. Q. J. Math. 57(4), 495\u2013504 (2006)","journal-title":"Q. J. Math."},{"issue":"2","key":"131_CR7","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.jcta.2009.06.001","volume":"117","author":"D Grynkiewicz","year":"2010","unstructured":"Grynkiewicz, D., Serra, O.: Properties of two-dimensional sets with small sumset. J. Combin. Theory Ser. A 117(2), 164\u2013188 (2010)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"3","key":"131_CR8","doi-asserted-by":"publisher","first-page":"1840","DOI":"10.1137\/18M1166067","volume":"32","author":"MA Hern\u00e1ndez Cifre","year":"2018","unstructured":"Hern\u00e1ndez Cifre, M.A., Iglesias, D., Yepes Nicol\u00e1s, J.: On a discrete Brunn\u2013Minkowski type inequality. SIAM J. Discrete Math. 32(3), 1840\u20131856 (2018)","journal-title":"SIAM J. Discrete Math."},{"key":"131_CR9","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.endm.2018.06.012","volume":"68","author":"M Huicochea","year":"2018","unstructured":"Huicochea, M.: Sums of finite subsets in $${\\mathbb{R}}^d$$. Electron. Notes Discret. Math. 68, 65\u201369 (2018)","journal-title":"Electron. Notes Discret. Math."},{"key":"131_CR10","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/S1385-7258(56)50032-7","volume":"18","author":"JHB Kemperman","year":"1956","unstructured":"Kemperman, J.H.B.: On complexes in a semigroup. Indag. Math. 18, 247\u2013254 (1956)","journal-title":"Indag. Math."},{"issue":"3","key":"131_CR11","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1112\/S002557931500042X","volume":"62","author":"BG Merino","year":"2016","unstructured":"Merino, B.G., Henze, M.: A generalization of the discrete version of Minkowski\u2019s fundamental theorem. Mathematika 62(3), 637\u2013652 (2016)","journal-title":"Mathematika"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00131-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-019-00131-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00131-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,27]],"date-time":"2020-08-27T23:10:17Z","timestamp":1598569817000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-019-00131-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,29]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["131"],"URL":"https:\/\/doi.org\/10.1007\/s00454-019-00131-9","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2019,8,29]]},"assertion":[{"value":"25 February 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 August 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 August 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}