{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T18:04:50Z","timestamp":1773252290982,"version":"3.50.1"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,11,19]],"date-time":"2015-11-19T00:00:00Z","timestamp":1447891200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2017,6]]},"DOI":"10.1007\/s10208-015-9300-x","type":"journal-article","created":{"date-parts":[[2015,11,19]],"date-time":"2015-11-19T20:52:08Z","timestamp":1447966328000},"page":"829-836","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Lower Bound for the Determinantal Complexity of a Hypersurface"],"prefix":"10.1007","volume":"17","author":[{"given":"Jarod","family":"Alper","sequence":"first","affiliation":[]},{"given":"Tristram","family":"Bogart","sequence":"additional","affiliation":[]},{"given":"Mauricio","family":"Velasco","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,19]]},"reference":[{"key":"9300_CR1","doi-asserted-by":"publisher","unstructured":"Leslie G. Valiant. Completeness classes in algebra. In Conference Record of the Eleventh Annual ACM Symposium on Theory of Computing (Atlanta, Ga.), pages 249\u2013261. 1979.","DOI":"10.1145\/800135.804419"},{"issue":"2","key":"9300_CR2","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/0304-3975(79)90044-6","volume":"8","author":"Leslie G Valiant","year":"1979","unstructured":"Leslie G. Valiant. The complexity of computing the permanent. Theoret. Comput. Sci., 8(2):189\u2013201, 1979.","journal-title":"Theoret. Comput. Sci."},{"key":"9300_CR3","doi-asserted-by":"publisher","first-page":"4241","DOI":"10.1155\/S1073792804142566","volume":"79","author":"Thierry Mignon","year":"2004","unstructured":"Thierry Mignon and Nicolas Ressayre. A quadratic bound for the determinant and permanent problem. Int. Math. Res. Not., (79):4241\u20134253, 2004.","journal-title":"Int. Math. Res. Not."},{"key":"9300_CR4","doi-asserted-by":"crossref","unstructured":"Jin-Yi Cai, Xi Chen, and Dong Li. A quadratic lower bound for the permanent and determinant problem over any characteristic $$\\ne 2$$ \u2260 2 . In STOC\u201908, pages 491\u2013497. ACM, New York, 2008.","DOI":"10.1145\/1374376.1374446"},{"key":"9300_CR5","unstructured":"Bruno Grenet. An Upper Bound for the Permanent versus Determinant Problem. to appear in Theory of Computing, 2011."},{"key":"9300_CR6","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0024-3795(87)90337-5","volume":"96","author":"Joachim von zur Gathen","year":"1987","unstructured":"Joachim von zur Gathen. Permanent and determinant. Linear Algebra Appl., 96:87\u2013100, 1987.","journal-title":"Linear Algebra Appl."},{"key":"9300_CR7","doi-asserted-by":"publisher","unstructured":"Roy Meshulam. On two extremal matrix problems. Linear Algebra and its Applications, 114115:261 \u2013 271, 1989.","DOI":"10.1016\/0024-3795(89)90465-5"},{"key":"9300_CR8","unstructured":"Jesko H\u00fcttenhain and Christian Ikenmeyer. Binary Determinantal Complexity. arXiv:1410.8202 [cs.CC], 2015."},{"key":"9300_CR9","unstructured":"David Eisenbud. Personal communication. 2015."},{"issue":"2","key":"9300_CR10","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1090\/S0002-9947-1921-1501168-0","volume":"22","author":"Leonard Eugene Dickson","year":"1921","unstructured":"Leonard Eugene Dickson. Determination of all general homogeneous polynomials expressible as determinants with linear elements. Trans. Amer. Math. Soc., 22(2):167\u2013179, 1921.","journal-title":"Trans. Amer. Math. Soc."},{"key":"9300_CR11","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1307\/mmj\/1030132707","volume":"48","author":"Arnaud Beauville","year":"2000","unstructured":"Arnaud Beauville. Determinantal hypersurfaces. Michigan Math. J., 48:39\u201364, 2000.","journal-title":"Michigan Math. J."},{"key":"9300_CR12","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1515\/crll.1863.62.265","volume":"62","author":"Heinrich Schr\u00f6ter","year":"1863","unstructured":"Heinrich Schr\u00f6ter. Nachweis der 27 geraden auf der allgemeinen oberfl\u00e4che dritter ordnung. J. Reine Angew. Math., 62:265\u2013280, 1863.","journal-title":"J. Reine Angew. Math."},{"key":"9300_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1515\/crll.1868.68.1","volume":"68","author":"Luigi Cremona","year":"1868","unstructured":"Luigi Cremona. M\u00e9moire de g\u00e9om\u00e9trie pure sur les surfaces du troisi\u00e8eme ordre. J. Reine Angew. Math., 68:1\u2013133, 1868.","journal-title":"J. Reine Angew. Math."},{"key":"9300_CR14","first-page":"49","volume":"49","author":"Hermann Grassmann","year":"1855","unstructured":"Hermann Grassmann. Die stereometrischen gleichungen dritten grades, und die dadurch erzeugten oberfl\u00e4chen. J. Reine Angew. Math., 49:49\u201365, 1855.","journal-title":"J. Reine Angew. Math."},{"issue":"3","key":"9300_CR15","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/BF01236873","volume":"3","author":"Michela Brundu","year":"1998","unstructured":"Michela Brundu and Alessandro Logar. Parametrization of the orbits of cubic surfaces. Transform. Groups, 3(3):209\u2013239, 1998.","journal-title":"Transform. Groups"},{"key":"9300_CR16","unstructured":"Joe Harris. Algebraic geometry, volume 133 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9300-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-015-9300-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9300-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9300-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,31]],"date-time":"2025-05-31T13:04:30Z","timestamp":1748696670000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-015-9300-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,19]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["9300"],"URL":"https:\/\/doi.org\/10.1007\/s10208-015-9300-x","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,19]]}}}