{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T21:02:39Z","timestamp":1772744559359,"version":"3.50.1"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100011019","name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","doi-asserted-by":"publisher","award":["PD125502"],"award-info":[{"award-number":["PD125502"]}],"id":[{"id":"10.13039\/501100011019","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003825","name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","doi-asserted-by":"publisher","award":["Bolyai \u00d6szt\u00f6nd\u00edj"],"award-info":[{"award-number":["Bolyai \u00d6szt\u00f6nd\u00edj"]}],"id":[{"id":"10.13039\/501100003825","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":["K132097"],"award-info":[{"award-number":["K132097"]}],"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":["K129335"],"award-info":[{"award-number":["K129335"]}],"id":[{"id":"10.13039\/501100011019","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":[[2022,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We improve the best known upper bound on the density of a planar measurable set <jats:italic>A<\/jats:italic> containing no two points at unit distance to 0.25442. We use a combination of Fourier analytic and linear programming methods to obtain the result. The estimate is achieved by means of obtaining new linear constraints on the autocorrelation function of\u00a0<jats:italic>A<\/jats:italic> utilizing triple-order correlations in\u00a0<jats:italic>A<\/jats:italic>, a concept that has not been previously studied.<\/jats:p>","DOI":"10.1007\/s00454-020-00263-3","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T17:04:02Z","timestamp":1607619842000},"page":"1245-1256","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Density Estimates of 1-Avoiding Sets via Higher Order Correlations"],"prefix":"10.1007","volume":"67","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1246-6601","authenticated-orcid":false,"given":"Gergely","family":"Ambrus","sequence":"first","affiliation":[]},{"given":"M\u00e1t\u00e9","family":"Matolcsi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"issue":"4","key":"263_CR1","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1007\/s00454-015-9668-z","volume":"53","author":"Ch Bachoc","year":"2015","unstructured":"Bachoc, Ch., Passuello, A., Thiery, A.: The density of sets avoiding distance $$1$$ in Euclidean space. Discrete Comput. Geom. 53(4), 783\u2013808 (2015)","journal-title":"Discrete Comput. Geom."},{"key":"263_CR2","unstructured":"Bellitto, T.: Walks, Transitions and Geometric Distances in Graphs. PhD thesis, Universit\u00e9 de Bordeaux (2018). https:\/\/www.labri.fr\/perso\/tbellitt\/tmp\/thesis.pdf"},{"key":"263_CR3","unstructured":"Bellitto, T., P\u00eacher, A., S\u00e9dillot, A.: On the density of sets of the Euclidean plane avoiding distance\u00a0$$1$$ (2018). arXiv:1810.00960"},{"key":"263_CR4","first-page":"22","volume":"30","author":"HT Croft","year":"1967","unstructured":"Croft, H.T.: Incidence incidents. Eureka 30, 22\u201326 (1967)","journal-title":"Eureka"},{"key":"263_CR5","doi-asserted-by":"publisher","unstructured":"DeCorte, E., de Oliveira Filho, F.M., Vallentin, F.: Complete positivity and distance-avoiding sets. Math. Program. (2020). https:\/\/doi.org\/10.1007\/s10107-020-01562-6","DOI":"10.1007\/s10107-020-01562-6"},{"key":"263_CR6","doi-asserted-by":"crossref","unstructured":"Erd\u0151s, P.: Problems and results in combinatorial geometry. In: Discrete Geometry and Convexity (New York 1982). Annals of the New York Academy of Sciences, vol. 440, pp. 1\u201311. New York Academy of Sciences, New York (1985)","DOI":"10.1111\/j.1749-6632.1985.tb14533.x"},{"issue":"1","key":"263_CR7","first-page":"18","volume":"28","author":"ADNJ de Grey","year":"2018","unstructured":"de Grey, A.D.N.J.: The chromatic number of the plane is at least 5. Geombinatorics 28(1), 18\u201331 (2018)","journal-title":"Geombinatorics"},{"issue":"3","key":"263_CR8","doi-asserted-by":"publisher","first-page":"642","DOI":"10.1007\/s00454-015-9751-5","volume":"55","author":"T Keleti","year":"2016","unstructured":"Keleti, T., Matolcsi, M., de Oliveira Filho, F.M., Ruzsa, I.Z.: Better bounds for planar sets avoiding unit distances. Discrete Comput. Geom. 55(3), 642\u2013661 (2016)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"263_CR9","first-page":"187","volume":"4","author":"L Moser","year":"1961","unstructured":"Moser, L., Moser, W.: Solution to problem 10. Can. Math. Bull. 4(2), 187\u2013189 (1961)","journal-title":"Can. Math. Bull."},{"issue":"6","key":"263_CR10","doi-asserted-by":"publisher","first-page":"1417","DOI":"10.4171\/JEMS\/236","volume":"12","author":"FM de Oliveira Filho","year":"2010","unstructured":"de Oliveira Filho, F.M., Vallentin, F.: Fourier analysis, linear programming, and densities of distance avoiding sets in $$\\mathbb{R}^n$$. J. Eur. Math. Soc. 12(6), 1417\u20131428 (2010)","journal-title":"J. Eur. Math. Soc."},{"key":"263_CR11","unstructured":"Sz\u00e9kely, L.A.: Erd\u0151s on unit distances and the Szemer\u00e9di\u2013Trotter theorems. In: Paul Erd\u0151s and His Mathematics (Budapest 1999), vol.\u00a02. Bolyai Soc. Math. Stud., vol.\u00a011, pp. 649\u2013666. Springer, Berlin (2002)"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00263-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-020-00263-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00263-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T14:07:15Z","timestamp":1652191635000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-020-00263-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,10]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["263"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00263-3","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,10]]},"assertion":[{"value":"23 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 October 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 December 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}