{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T19:24:49Z","timestamp":1774380289337,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T00:00:00Z","timestamp":1613433600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T00:00:00Z","timestamp":1613433600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100011199","name":"FP7 Ideas: European Research Council","doi-asserted-by":"publisher","award":["615640"],"award-info":[{"award-number":["615640"]}],"id":[{"id":"10.13039\/100011199","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100011199","name":"FP7 Ideas: European Research Council","doi-asserted-by":"publisher","award":["615640"],"award-info":[{"award-number":["615640"]}],"id":[{"id":"10.13039\/100011199","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1740425"],"award-info":[{"award-number":["CCF-1740425"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1740425"],"award-info":[{"award-number":["CCF-1740425"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1740425"],"award-info":[{"award-number":["CCF-1740425"]}],"id":[{"id":"10.13039\/100000001","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":[[2021,4]]},"DOI":"10.1007\/s00454-020-00181-4","type":"journal-article","created":{"date-parts":[[2021,2,19]],"date-time":"2021-02-19T12:33:09Z","timestamp":1613737989000},"page":"587-600","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bounds on the Number of 2-Level Polytopes, Cones, and Configurations"],"prefix":"10.1007","volume":"65","author":[{"given":"Samuel","family":"Fiorini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Macchia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kanstantsin","family":"Pashkovich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,16]]},"reference":[{"issue":"3","key":"181_CR1","doi-asserted-by":"publisher","first-page":"1857","DOI":"10.1137\/17M1116684","volume":"32","author":"M Aprile","year":"2018","unstructured":"Aprile, M., Cevallos, A., Faenza, Y.: On 2-level polytopes arising in combinatorial settings. SIAM J. Discrete Math. 32(3), 1857\u20131886 (2018)","journal-title":"SIAM J. Discrete Math."},{"key":"181_CR2","first-page":"147","volume":"5","author":"G Birkhoff","year":"1946","unstructured":"Birkhoff, G.: Tres observaciones sobre el algebra lineal. Univ. Nac. Tucum\u00e1n Rev. Ser. A 5, 147\u2013151 (1946)","journal-title":"Univ. Nac. Tucum\u00e1n Rev. Ser. A"},{"key":"181_CR3","unstructured":"Bohn, A., Faenza, Yu., Fiorini, S., Fisikopoulos, V., Macchia, M., Pashkovich, K.: Enumeration of 2-level polytopes (2017). arXiv:1703.01943"},{"key":"181_CR4","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/0095-8956(75)90041-6","volume":"18","author":"V Chv\u00e1tal","year":"1975","unstructured":"Chv\u00e1tal, V.: On certain polytopes associated with graphs. J. Comb. Theory Ser. B 18, 138\u2013154 (1975)","journal-title":"J. Comb. Theory Ser. B"},{"key":"181_CR5","series-title":"Algorithms and Combinatorics","volume-title":"Geometry of Cuts and Metrics","author":"MM Deza","year":"2009","unstructured":"Deza, M.M., Laurent, M.: Geometry of Cuts and Metrics. Algorithms and Combinatorics. Springer, Berlin (2009)"},{"key":"181_CR6","unstructured":"Erd\u0151s, P., Kleitman, D.J., Rothschild, B.L.: Asymptotic enumeration of $$K_n$$-free graphs. In: Colloquio Internazionale sulle Teorie Combinatorie, vol. II. Atti dei Convegni Lincei, vol. 17, pp. 19\u201327. Accademia Nazionale dei Lincei, Rome (1976)"},{"issue":"10","key":"181_CR7","doi-asserted-by":"publisher","first-page":"2921","DOI":"10.1016\/j.laa.2013.08.009","volume":"439","author":"J Gouveia","year":"2013","unstructured":"Gouveia, J., Grappe, R., Kaibel, V., Pashkovich, K., Robinson, R.Z., Thomas, R.R.: Which nonnegative matrices are slack matrices? Linear Algebra Appl. 439(10), 2921\u20132933 (2013)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"181_CR8","doi-asserted-by":"publisher","first-page":"2097","DOI":"10.1137\/090746525","volume":"20","author":"J Gouveia","year":"2010","unstructured":"Gouveia, J., Parrilo, P.A., Thomas, R.R.: Theta bodies for polynomial ideals. SIAM J. Optim. 20(4), 2097\u20132118 (2010)","journal-title":"SIAM J. Optim."},{"key":"181_CR9","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1016\/j.jcta.2016.08.002","volume":"145","author":"J Gouveia","year":"2017","unstructured":"Gouveia, J., Pashkovich, K., Robinson, R.Z., Thomas, R.R.: Four-dimensional polytopes of minimum positive semidefinite rank. J. Comb. Theory Ser. A 145, 184\u2013226 (2017)","journal-title":"J. Comb. Theory Ser. A"},{"issue":"3","key":"181_CR10","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1007\/s00454-013-9533-x","volume":"50","author":"J Gouveia","year":"2013","unstructured":"Gouveia, J., Robinson, R.Z., Thomas, R.R.: Polytopes of minimum positive semidefinite rank. Discrete Comput. Geom. 50(3), 679\u2013699 (2013)","journal-title":"Discrete Comput. Geom."},{"key":"181_CR11","unstructured":"Grande, F.: On $$k$$-Level Matroids: Geometry and Combinatorics. PhD thesis, Freie Universit\u00e4t Berlin (2015)"},{"issue":"4","key":"181_CR12","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1007\/s00454-015-9735-5","volume":"54","author":"F Grande","year":"2015","unstructured":"Grande, F., Ru\u00e9, J.: Many 2-level polytopes from matroids. Discrete Comput. Geom. 54(4), 954\u2013979 (2015)","journal-title":"Discrete Comput. Geom."},{"key":"181_CR13","doi-asserted-by":"publisher","first-page":"65","DOI":"10.7146\/math.scand.a-10456","volume":"4","author":"O Hanner","year":"1956","unstructured":"Hanner, O.: Intersections of translates of convex bodies. Math. Scand. 4, 65\u201387 (1956)","journal-title":"Math. Scand."},{"key":"181_CR14","volume-title":"Communication Complexity","author":"E Kushilevitz","year":"1997","unstructured":"Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)"},{"key":"181_CR15","volume-title":"Lower Bounds in Communication Complexity","author":"T Lee","year":"2009","unstructured":"Lee, T., Shraibman, A.: Lower Bounds in Communication Complexity. Now Publishers, Hanover (2009)"},{"issue":"2","key":"181_CR16","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1016\/0022-0000(93)90035-U","volume":"47","author":"L Lov\u00e1sz","year":"1993","unstructured":"Lov\u00e1sz, L., Saks, M.: Communication complexity and combinatorial lattice theory. J. Comput. Syst. Sci. 47(2), 322\u2013349 (1993)","journal-title":"J. Comput. Syst. Sci."},{"key":"181_CR17","unstructured":"Macchia, M.: Two Level Polytopes: Geometry and Optimization. PhD thesis, Universit\u00e9 Libre de Bruxelles (2018)"},{"key":"181_CR18","series-title":"Wiley-Interscience Series in Discrete Mathematics","volume-title":"Theory of Linear and Integer Programming","author":"A Schrijver","year":"1986","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. Wiley-Interscience Series in Discrete Mathematics. Wiley, Chichester (1986)"},{"issue":"1","key":"181_CR19","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/BF02187680","volume":"1","author":"RP Stanley","year":"1986","unstructured":"Stanley, R.P.: Two poset polytopes. Discrete Comput. Geom. 1(1), 9\u201323 (1986)","journal-title":"Discrete Comput. Geom."},{"issue":"3","key":"181_CR20","doi-asserted-by":"publisher","first-page":"433","DOI":"10.2748\/tmj\/1163775139","volume":"58","author":"S Sullivant","year":"2006","unstructured":"Sullivant, S.: Compressed polytopes and statistical disclosure limitation. Tohoku Math. J. 58(3), 433\u2013445 (2006)","journal-title":"Tohoku Math. J."},{"issue":"3","key":"181_CR21","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/0022-0000(91)90024-Y","volume":"43","author":"M Yannakakis","year":"1991","unstructured":"Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. J. Comput. Syst. Sci. 43(3), 441\u2013466 (1991)","journal-title":"J. Comput. Syst. Sci."},{"key":"181_CR22","doi-asserted-by":"crossref","unstructured":"Yao, A.C.: Some complexity questions related to distributed computing. In: Proceedings of the 11th Annual ACM Symposium on Theory of Computing (STOC\u201979), pp. 209\u2013213. ACM, New York (1979)","DOI":"10.1145\/800135.804414"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00181-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-020-00181-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00181-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T20:13:46Z","timestamp":1614975226000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-020-00181-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,16]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["181"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00181-4","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,16]]},"assertion":[{"value":"15 June 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 January 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}