{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T14:40:22Z","timestamp":1731681622156,"version":"3.28.0"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T00:00:00Z","timestamp":1720656000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T00:00:00Z","timestamp":1720656000000},"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":["Combinatorica"],"published-print":{"date-parts":[[2024,12]]},"DOI":"10.1007\/s00493-024-00112-4","type":"journal-article","created":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T13:01:56Z","timestamp":1720702916000},"page":"1169-1176","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Unavoidable Flats in Matroids Representable over Prime Fields"],"prefix":"10.1007","volume":"44","author":[{"given":"Jim","family":"Geelen","sequence":"first","affiliation":[]},{"given":"Matthew E.","family":"Kroeker","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,11]]},"reference":[{"key":"112_CR1","doi-asserted-by":"crossref","unstructured":"Barak, B., Dvir, Z., Wigderson, A., Yehudayoff, A.: Rank bounds for design matrices with applications to combinatorial geometry and locally correctable codes. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, STOC 2011, San Jose, CA, pp. 519\u2013528. ACM, New York (2011)","DOI":"10.1145\/1993636.1993705"},{"key":"112_CR2","first-page":"638","volume":"2011","author":"A Bhattacharyya","year":"2011","unstructured":"Bhattacharyya, A., Dvir, Z., Shpilka, A., Saraf, S.: Tight lower bounds for 2-query LCCs over finite fields. Proc. FOCS 2011, 638\u2013647 (2011)","journal-title":"Proc. FOCS"},{"key":"112_CR3","first-page":"11","volume":"15","author":"W Bonnice","year":"1967","unstructured":"Bonnice, W., Edelstein, M.: Flats associated with the finite sets in $$\\mathbb{P} ^d$$. Nieuw Archief voor Wiskunde 15, 11\u201314 (1967)","journal-title":"Nieuw Archief voor Wiskunde"},{"key":"112_CR4","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF02112289","volume":"40","author":"P Borwein","year":"1990","unstructured":"Borwein, P., Moser, W.O.J.: A survey of Sylvester\u2019s problem and its generalizations. Aequationes Mathematicae 40, 111\u2013135 (1990)","journal-title":"Aequationes Mathematicae"},{"key":"112_CR5","volume-title":"Improved Rank Bounds for Design Matrices and a New Proof of Kelly\u2019s Theorem. Forum of Mathematics, Sigma","author":"Z Dvir","year":"2014","unstructured":"Dvir, Z., Saraf, S., Wigderson, A.: Improved Rank Bounds for Design Matrices and a New Proof of Kelly\u2019s Theorem. Forum of Mathematics, Sigma, vol. 2. Cambridge University Press, Cambridge (2014)"},{"key":"112_CR6","doi-asserted-by":"crossref","first-page":"169","DOI":"10.2307\/2303021","volume":"51","author":"T Gallai","year":"1944","unstructured":"Gallai, T.: Solution to Problem 4065. Am. Math. Mon. 51, 169\u2013171 (1944)","journal-title":"Am. Math. Mon."},{"key":"112_CR7","unstructured":"Geelen, J., Kroeker, M.E.: A Sylvester-Gallai-type theorem for complex-representable matroids. arXiv preprint arXiv:2212.03307 (2022)"},{"issue":"3","key":"112_CR8","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1016\/0001-8708(72)90005-9","volume":"8","author":"RL Graham","year":"1972","unstructured":"Graham, R.L., Leeb, K., Rothschild, B.L.: Ramsey\u2019s theorem for a class of categories. Adv. Math. 8(3), 417\u2013433 (1972)","journal-title":"Adv. Math."},{"issue":"2","key":"112_CR9","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1090\/S0002-9947-1963-0143712-1","volume":"106","author":"AW Hales","year":"1963","unstructured":"Hales, A.W., Jewett, R.I.: Regularity and positional games. Trans. Am. Math. Soc. 106(2), 222\u2013229 (1963)","journal-title":"Trans. Am. Math. Soc."},{"key":"112_CR10","doi-asserted-by":"publisher","first-page":"175","DOI":"10.7146\/math.scand.a-10758","volume":"16","author":"S Hansen","year":"1965","unstructured":"Hansen, S.: A generalization of a theorem of Sylvester on the lines determined by a finite point set. Mathematica Scandinavica 16, 175\u2013180 (1965)","journal-title":"Mathematica Scandinavica"},{"key":"112_CR11","doi-asserted-by":"crossref","unstructured":"Hirzebruch, F.: Arrangements of lines and algebraic surfaces. In: Arithmetic and Geometry (Papers dedicated to I. R. Shafarevich), vol. 2, pp. 113\u2013140, Birkhauser (1983)","DOI":"10.1007\/978-1-4757-9286-7_7"},{"key":"112_CR12","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/BF02187687","volume":"1","author":"LM Kelly","year":"1986","unstructured":"Kelly, L.M.: A resolution of the Sylvester-Gallai problem of J.-P. Serre Discret. Comput. Geom. 1, 101\u2013104 (1986)","journal-title":"Serre Discret. Comput. Geom."},{"issue":"1","key":"112_CR13","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/0095-8956(90)90095-H","volume":"50","author":"JPS Kung","year":"1990","unstructured":"Kung, J.P.S.: The long-line graph of a combinatorial geometry. II. Geometries representable over two fields of different characteristics. J. Comb. Theory Ser. B 50(1), 41\u201353 (1990)","journal-title":"J. Comb. Theory Ser. B"},{"issue":"1","key":"112_CR14","first-page":"461","volume":"5","author":"E Melchior","year":"1941","unstructured":"Melchior, E.: \u00dcber vielseite der projektiven ebene. Deutsche Mathematik 5(1), 461\u2013475 (1941)","journal-title":"Deutsche Mathematik"},{"key":"112_CR15","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/BF01817744","volume":"4","author":"USR Murty","year":"1970","unstructured":"Murty, U.S.R.: Matroids with Sylvester property. Aequationes Mathematicae 4, 44\u201350 (1970)","journal-title":"Aequationes Mathematicae"},{"key":"112_CR16","first-page":"98","volume":"59","author":"JJ Sylvester","year":"1893","unstructured":"Sylvester, J.J.: Mathematical question 11851. Educ. Times 59, 98 (1893)","journal-title":"Educ. Times"}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-024-00112-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-024-00112-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-024-00112-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T14:03:36Z","timestamp":1731679416000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-024-00112-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,11]]},"references-count":16,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["112"],"URL":"https:\/\/doi.org\/10.1007\/s00493-024-00112-4","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"type":"print","value":"0209-9683"},{"type":"electronic","value":"1439-6912"}],"subject":[],"published":{"date-parts":[[2024,7,11]]},"assertion":[{"value":"27 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 May 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 June 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 July 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}