{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:13Z","timestamp":1740109573088,"version":"3.37.3"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,4,9]],"date-time":"2019-04-09T00:00:00Z","timestamp":1554768000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,4,9]],"date-time":"2019-04-09T00:00:00Z","timestamp":1554768000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["314838170, GRK 2297"],"award-info":[{"award-number":["314838170, GRK 2297"]}],"id":[{"id":"10.13039\/501100001659","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":[[2021,1]]},"DOI":"10.1007\/s00454-019-00089-8","type":"journal-article","created":{"date-parts":[[2019,4,10]],"date-time":"2019-04-10T16:28:38Z","timestamp":1554913718000},"page":"212-226","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Equality Case in van der Corput\u2019s Inequality and Collisions in Multiple Lattice Tilings"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2245-9958","authenticated-orcid":false,"given":"Gennadiy","family":"Averkov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,4,9]]},"reference":[{"key":"89_CR1","unstructured":"Averkov, G.: Local optimality of Zaks\u2013Perles\u2013Wills simplices (2018). arXiv:1803.04852"},{"key":"89_CR2","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1016\/j.aim.2014.12.035","volume":"274","author":"G Averkov","year":"2015","unstructured":"Averkov, G., Kr\u00fcmpelmann, J., Nill, B.: Largest integral simplices with one interior integral point: solution of Hensley\u2019s conjecture and related results. Adv. Math. 274, 118\u2013166 (2015)","journal-title":"Adv. Math."},{"key":"89_CR3","doi-asserted-by":"publisher","unstructured":"Averkov, G., Kr\u00fcmpelmann, J., Nill, B.: Lattice simplices with a fixed positive number of interior lattice points: A nearly optimal volume bound. Int. Math. Res. Not. https:\/\/doi.org\/10.1093\/imrn\/rny130.arXiv:1710.08646","DOI":"10.1093\/imrn\/rny130."},{"key":"89_CR4","unstructured":"Balletti, G., Kasprzyk, A.M.: Three-dimensional lattice polytopes with two interior lattice points (2016). arXiv:1612.08918"},{"key":"89_CR5","series-title":"Colloquia Mathematica Societatis J\u00e1nos Bolyai","first-page":"39","volume-title":"Intuitive Geometry (Szeged, 1991)","author":"U Bolle","year":"1994","unstructured":"Bolle, U.: On multiple tiles in $$E^2$$. In: B\u00f6r\u00f6czky, K., Fejes T\u00f3th, G. (eds.) Intuitive Geometry (Szeged, 1991). Colloquia Mathematica Societatis J\u00e1nos Bolyai, vol. 63, pp. 39\u201343. North-Holland, Amsterdam (1994)"},{"key":"89_CR6","series-title":"Classics in Mathematics","volume-title":"An Introduction to the Geometry of Numbers","author":"JWS Cassels","year":"1997","unstructured":"Cassels, J.W.S.: An Introduction to the Geometry of Numbers. Classics in Mathematics. Springer, Berlin (1997). Corrected reprint of the 1971 edition"},{"issue":"3","key":"89_CR7","doi-asserted-by":"publisher","first-page":"1104","DOI":"10.1137\/120877635","volume":"26","author":"J Draisma","year":"2012","unstructured":"Draisma, J., McAllister, T.B., Nill, B.: Lattice-width directions and Minkowski\u2019s $$3^d$$-theorem. SIAM J. Discrete Math. 26(3), 1104\u20131107 (2012)","journal-title":"SIAM J. Discrete Math."},{"key":"89_CR8","first-page":"125","volume-title":"Number Theory, Vol. I (Budapest, 1987). Colloquia Mathematica Societatis J\u00e1nos Bolyai","author":"G Freiman","year":"1990","unstructured":"Freiman, G., Heppes, A., Uhrin, B.: A lower estimation for the cardinality of finite difference sets in $${\\bf R}^n$$. In: Gy\u00f6ry, K., Hal\u00e1sz, G. (eds.) Number Theory, Vol. I (Budapest, 1987). Colloquia Mathematica Societatis J\u00e1nos Bolyai, pp. 125\u2013139. North-Holland, Amsterdam (1990)"},{"issue":"3","key":"89_CR9","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1112\/S002557931500042X","volume":"62","author":"B Gonz\u00e1lez Merino","year":"2016","unstructured":"Gonz\u00e1lez Merino, B., Henze, M.: A generalization of the discrete version of Minkowski\u2019s fundamental theorem. Mathematika 62(3), 637\u2013652 (2016)","journal-title":"Mathematika"},{"issue":"6","key":"89_CR10","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1007\/s00493-012-2860-3","volume":"32","author":"N Gravin","year":"2012","unstructured":"Gravin, N., Robins, S., Shiryaev, D.: Translational tilings by a polytope, with multiplicity. Combinatorica 32(6), 629\u2013649 (2012)","journal-title":"Combinatorica"},{"key":"89_CR11","volume-title":"Convex and Discrete Geometry. Grundlehren der Mathematischen Wissenschaften","author":"PM Gruber","year":"2007","unstructured":"Gruber, P.M.: Convex and Discrete Geometry. Grundlehren der Mathematischen Wissenschaften, vol. 336. Springer, Berlin (2007)"},{"key":"89_CR12","series-title":"North-Holland Mathematical Library","volume-title":"Geometry of Numbers","author":"PM Gruber","year":"1987","unstructured":"Gruber, P.M., Lekkerkerker, C.G.: Geometry of Numbers. North-Holland Mathematical Library, vol. 37, 2nd edn. North-Holland, Amsterdam (1987)","edition":"2"},{"issue":"1","key":"89_CR13","doi-asserted-by":"publisher","first-page":"183","DOI":"10.2140\/pjm.1983.105.183","volume":"105","author":"D Hensley","year":"1983","unstructured":"Hensley, D.: Lattice vertex polytopes with interior lattice points. Pac. J. Math. 105(1), 183\u2013191 (1983)","journal-title":"Pac. J. Math."},{"issue":"5","key":"89_CR14","doi-asserted-by":"publisher","first-page":"1022","DOI":"10.4153\/CJM-1991-058-4","volume":"43","author":"JC Lagarias","year":"1991","unstructured":"Lagarias, J.C., Ziegler, G.M.: Bounds for lattice polytopes containing a fixed number of interior points in a sublattice. Can. J. Math. 43(5), 1022\u20131035 (1991)","journal-title":"Can. J. Math."},{"issue":"1\u20132","key":"89_CR15","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1112\/S0025579300014339","volume":"48","author":"O Pikhurko","year":"2001","unstructured":"Pikhurko, O.: Lattice points in lattice polytopes. Mathematika 48(1\u20132), 15\u201324 (2001)","journal-title":"Mathematika"},{"key":"89_CR16","volume-title":"Convex Bodies: the Brunn\u2013Minkowski Theory. Encyclopedia of Mathematics and Its Applications, vol. 151, expanded edn.","author":"R Schneider","year":"2014","unstructured":"Schneider, R.: Convex Bodies: the Brunn\u2013Minkowski Theory. Encyclopedia of Mathematics and Its Applications, vol. 151, expanded edn. Cambridge University Press, Cambridge (2014)"},{"issue":"2","key":"89_CR17","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1016\/0022-314X(81)90004-4","volume":"13","author":"B Uhrin","year":"1981","unstructured":"Uhrin, B.: On a generalization of Minkowski\u2019s convex body theorem. J. Number Theory 13(2), 192\u2013209 (1981)","journal-title":"J. Number Theory"},{"key":"89_CR18","unstructured":"Yang, Q., Zong, C.: Multiple lattice tilings in Euclidean spaces (2017). arXiv:1710.05506"},{"key":"89_CR19","unstructured":"Yang, Q., Zong, C.: Multiple translative tilings in Euclidean spaces (2017). arXiv:1711.02514"},{"key":"89_CR20","unstructured":"Zong, C.: Characterization of the two-dimensional five-fold lattice tiles (2017). arXiv:1712.01122"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00089-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-019-00089-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00089-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,3]],"date-time":"2021-01-03T19:12:54Z","timestamp":1609701174000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-019-00089-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,9]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["89"],"URL":"https:\/\/doi.org\/10.1007\/s00454-019-00089-8","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2019,4,9]]},"assertion":[{"value":"20 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 February 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 April 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}