{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:29Z","timestamp":1740109589573,"version":"3.37.3"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T00:00:00Z","timestamp":1706918400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T00:00:00Z","timestamp":1706918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["34180"],"award-info":[{"award-number":["34180"]}],"id":[{"id":"10.13039\/501100002428","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":[[2025,3]]},"DOI":"10.1007\/s00454-023-00625-7","type":"journal-article","created":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T22:02:09Z","timestamp":1706997729000},"page":"437-446","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convexity, Elementary Methods, and Distances"],"prefix":"10.1007","volume":"73","author":[{"given":"Oliver","family":"Roche-Newton","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8092-577X","authenticated-orcid":false,"given":"Dmitrii","family":"Zhelezov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,2,3]]},"reference":[{"issue":"4","key":"625_CR1","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1007\/s00493-023-00035-6","volume":"43","author":"PJ Bradshaw","year":"2023","unstructured":"Bradshaw, P.J.: Growth in sumsets of higher convex functions. Combinatorica 43(4), 769\u2013789 (2023)","journal-title":"Combinatorica"},{"key":"625_CR2","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/0012-365X(86)90009-9","volume":"60","author":"P Erd\u0151s","year":"1986","unstructured":"Erd\u0151s, P.: On some metric and combinatorial geometric problems. Discrete Math. 60, 147\u2013153 (1986)","journal-title":"Discrete Math."},{"issue":"1","key":"625_CR3","doi-asserted-by":"publisher","first-page":"155","DOI":"10.4007\/annals.2015.181.1.2","volume":"181","author":"L Guth","year":"2015","unstructured":"Guth, L., Katz, N.H.: On the Erd\u0151s distinct distance problem in the plane. Ann. Math. 181(1), 155\u2013190 (2015)","journal-title":"Ann. Math."},{"issue":"5","key":"625_CR4","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1007\/s00493-016-3665-6","volume":"38","author":"B Hanson","year":"2018","unstructured":"Hanson, B.: The additive structure of Cartesian products spanning few distinct distances. Combinatorica 38(5), 1095\u20131100 (2018)","journal-title":"Combinatorica"},{"issue":"1","key":"625_CR5","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s00493-021-4578-6","volume":"42","author":"B Hanson","year":"2022","unstructured":"Hanson, B., Roche-Newton, O., Rudnev, M.: Higher convexity and iterated sum sets. Combinatorica 42(1), 71\u201385 (2022)","journal-title":"Combinatorica"},{"issue":"5","key":"625_CR6","doi-asserted-by":"publisher","first-page":"1900","DOI":"10.1112\/jlms.12728","volume":"107","author":"B Hanson","year":"2023","unstructured":"Hanson, B., Roche-Newton, O., Senger, S.: Convexity, superquadratic growth, and dot products. J. Lond. Math. Soc. 107(5), 1900\u20131923 (2023)","journal-title":"J. Lond. Math. Soc."},{"key":"625_CR7","unstructured":"Mudgal, A.: Energy estimates in sum-product and convexity problems. arXiv:2109.04932"},{"issue":"1","key":"625_CR8","doi-asserted-by":"publisher","first-page":"1.7, 7","DOI":"10.37236\/7736","volume":"26","author":"C Pohoata","year":"2019","unstructured":"Pohoata, C.: On Cartesian products which determine few distinct distances. Electron. J. Combin. 26(1), 1.7, 7 (2019)","journal-title":"Electron. J. Combin."},{"key":"625_CR9","doi-asserted-by":"crossref","unstructured":"Ruzsa, I.Z., Shakan, G., Solymosi, J., Szemer\u00e9di, E.: \u2018On distinct consecutive differences\u2019, Combinatorial and additive number theory IV 425-434, Springer Proceedings in Mathematics Statistics, 347, Springer, Cham (2021)","DOI":"10.1007\/978-3-030-67996-5_24"},{"issue":"1","key":"625_CR10","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1090\/S0273-0979-2012-01392-7","volume":"50","author":"T Sanders","year":"2013","unstructured":"Sanders, T.: The structure theory of set addition revisited. Bull. Am. Math. Soc (N. S.) 50(1), 93\u2013127 (2013)","journal-title":"Bull. Am. Math. Soc (N. S.)"},{"issue":"1","key":"625_CR11","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s00493-008-2099-1","volume":"28","author":"J Solymosi","year":"2008","unstructured":"Solymosi, J., Vu, V.: Near optimal bounds for the Erd\u0151s distinct distances problem in high dimensions. Combinatorica 28(1), 113\u2013125 (2008)","journal-title":"Combinatorica"},{"key":"625_CR12","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1016\/j.aim.2008.05.002","volume":"219","author":"T Tao","year":"2018","unstructured":"Tao, T., Vu, V.: John-type theorems for generalized arithmetic progressions and iterated sumsets. Adv. Math. 219, 428\u2013449 (2018)","journal-title":"Adv. Math."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-023-00625-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-023-00625-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-023-00625-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T23:52:46Z","timestamp":1739836366000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-023-00625-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,3]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["625"],"URL":"https:\/\/doi.org\/10.1007\/s00454-023-00625-7","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2024,2,3]]},"assertion":[{"value":"16 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 December 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}