{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T02:19:43Z","timestamp":1770776383544,"version":"3.50.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T00:00:00Z","timestamp":1741392000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T00:00:00Z","timestamp":1741392000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2025,4]]},"DOI":"10.1007\/s00454-025-00727-4","type":"journal-article","created":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T18:38:36Z","timestamp":1741459116000},"page":"618-628","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Smallest Density of Non-Separable Lattices"],"prefix":"10.1007","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2091-7946","authenticated-orcid":false,"given":"Arkadiy","family":"Aliev","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,8]]},"reference":[{"issue":"6","key":"727_CR1","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1080\/10556788.2010.547580","volume":"27","author":"T Bayen","year":"2012","unstructured":"Bayen, T., Henrion, D.: Semidefinite programming for optimizing convex bodies under width constraints. Optim. Methods Softw. 27(6), 1073\u20131099 (2012)","journal-title":"Optim. Methods Softw."},{"key":"727_CR2","series-title":"Die Grundlehren der mathematischen Wissenschaften","volume-title":"An Introduction to the Geometry of Numbers","author":"JWS Cassels","year":"1971","unstructured":"Cassels, J.W.S.: An Introduction to the Geometry of Numbers. Die Grundlehren der mathematischen Wissenschaften, vol. 99. Springer, Berlin (1971)"},{"key":"727_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082079","volume-title":"Geometry of Banach Spaces\u2014Selected Topics","author":"J Diestel","year":"1975","unstructured":"Diestel, J.: Geometry of Banach Spaces\u2014Selected Topics, vol. 485. Springer, Berlin (1975)"},{"key":"727_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2020.103906","volume":"151","author":"A Fidlin","year":"2020","unstructured":"Fidlin, A., R\u00f6mer, U., Seemann, W.: The normal parameterization and its application to collision detection. Mech. Mach. Theory 151, 103906 (2020). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2020.103906","journal-title":"Mech. Mach. Theory"},{"key":"727_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107341029","volume-title":"Geometric Tomography","author":"RJ Gardner","year":"2006","unstructured":"Gardner, R.J.: Geometric Tomography, 2nd edn. Cambridge University Press, Cambridge (2006)","edition":"2"},{"key":"727_CR6","volume-title":"Convex and Discrete Geometry","author":"P Gruber","year":"2007","unstructured":"Gruber, P.: Convex and Discrete Geometry. Springer, Berlin (2007)"},{"key":"727_CR7","doi-asserted-by":"publisher","first-page":"287","DOI":"10.48550\/arXiv.1103.4518","volume":"39","author":"T Hales","year":"2011","unstructured":"Hales, T.: On the Reinhardt Conjecture, Vietnam. J. Math. 39, 287\u2013307 (2011). https:\/\/doi.org\/10.48550\/arXiv.1103.4518","journal-title":"J. Math."},{"issue":"3","key":"727_CR8","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1215\/20088752-2017-0001","volume":"8","author":"GM Ivanov","year":"2017","unstructured":"Ivanov, G.M., Martini, H.: New moduli for Banach spaces. Ann. Funct. Anal. 8(3), 350\u2013365 (2017)","journal-title":"Ann. Funct. Anal."},{"key":"727_CR9","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1112\/jlms\/s2-40.2.369","volume":"40","author":"M Lassak","year":"1989","unstructured":"Lassak, M.: Approximation of plane convex bodies by centrally symmetric bodies. J. Lond. Math. Soc. S2 40, 369\u2013377 (1989)","journal-title":"J. Lond. Math. Soc. S2"},{"key":"727_CR10","first-page":"19","volume":"13","author":"E Makai","year":"1978","unstructured":"Makai, E.: On the thinnest non-separable lattice of convex bodies. Stud. Sci. Math. Hung. 13, 19\u201327 (1978)","journal-title":"Stud. Sci. Math. Hung."},{"key":"727_CR11","unstructured":"Makai, E., Martini, H.: Density estimates for $$k$$-impassable lattices of balls and general convex bodies in $${\\mathbb{R}}^{n}$$ (2016). https:\/\/arxiv.org\/abs\/1612.01307"},{"key":"727_CR12","first-page":"191","volume":"9","author":"E Makai","year":"1974","unstructured":"Makai, E., T\u00f3th, L.F.: On the thinnest non-separable lattice of convex plates. Stud. Sci. Math. Hung. 9, 191 (1974)","journal-title":"Stud. Sci. Math. Hung."},{"key":"727_CR13","unstructured":"Petty, C.M.: Isoperimetric problems. In: Proceedings of the Conference on Convexity and Combinatorial Geometry, pp. 26\u201341 (1971)"},{"key":"727_CR14","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/BF02940676","volume":"10","author":"K Reinhardt","year":"1934","unstructured":"Reinhardt, K.: \u00dcber die dichteste gitterf \u00f6rmige lagerung kongruenter bereiche in der ebene und eine besondere art konvexer kurven. Abh. Math. Semin. Univ. Hambg. 10, 216\u2013230 (1934). https:\/\/doi.org\/10.1007\/BF02940676","journal-title":"Abh. Math. Semin. Univ. Hambg."},{"key":"727_CR15","unstructured":"Reshetnyak, Y.G.: An extremal problem from the theory of convex curves. Uspekhi Matematicheskikh Nauk 8(6(58)):125\u2013126 (1953) (in Russian)"},{"issue":"3","key":"727_CR16","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1007\/bf02844505","volume":"33","author":"R Schneider","year":"1984","unstructured":"Schneider, R.: Smooth approximation of convex bodies. Rendiconti Del Circolo Matematico Di Palermo 33(3), 436\u2013440 (1984). https:\/\/doi.org\/10.1007\/bf02844505","journal-title":"Rendiconti Del Circolo Matematico Di Palermo"},{"key":"727_CR17","series-title":"Encyclopedia of Mathematics and Its Applications","volume-title":"Convex Bodies: The Brunn-Minkowski Theory, Second Expanded Edition","author":"R Schneider","year":"2014","unstructured":"Schneider, R.: Convex Bodies: The Brunn-Minkowski Theory, Second Expanded Edition. Encyclopedia of Mathematics and Its Applications, vol. 151. Cambridge University Press, Cambridge (2014)"},{"key":"727_CR18","first-page":"103","volume":"12","author":"P Tammela","year":"1970","unstructured":"Tammela, P.: An estimate of the critical determinant of a two dimensional convex symmetric domain. Izv. Vys\u0161. U\u010debn. Zaved. Mat. 12, 103\u2013107 (1970). (in Russian)","journal-title":"Izv. Vys\u0161. U\u010debn. Zaved. Mat."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-025-00727-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-025-00727-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-025-00727-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T14:58:24Z","timestamp":1742223504000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-025-00727-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,8]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["727"],"URL":"https:\/\/doi.org\/10.1007\/s00454-025-00727-4","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,8]]},"assertion":[{"value":"27 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 February 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}