{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:22Z","timestamp":1740109582975,"version":"3.37.3"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T00:00:00Z","timestamp":1638316800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T00:00:00Z","timestamp":1638316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/MAT\/00324\/2019"],"award-info":[{"award-number":["UID\/MAT\/00324\/2019"]}],"id":[{"id":"10.13039\/501100001871","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":[[2022,3]]},"DOI":"10.1007\/s00454-021-00347-8","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T22:02:56Z","timestamp":1638396176000},"page":"462-491","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Algebraic Approach to Projective Uniqueness with an Application to Order Polytopes"],"prefix":"10.1007","volume":"67","author":[{"given":"Tristram","family":"Bogart","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8345-9754","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Gouveia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Camilo","family":"Torres","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,12,1]]},"reference":[{"issue":"3","key":"347_CR1","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1007\/s00222-014-0519-y","volume":"199","author":"KA Adiprasito","year":"2015","unstructured":"Adiprasito, K.A., Ziegler, G.M.: Many projectively unique polytopes. Invent. Math. 199(3), 581\u2013652 (2015)","journal-title":"Invent. Math."},{"issue":"3","key":"347_CR2","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."},{"issue":"1","key":"347_CR3","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s12532-018-0145-6","volume":"11","author":"A Bohn","year":"2019","unstructured":"Bohn, A., Faenza, Y., Fiorini, S., Fisikopoulos, V., Macchia, M., Pashkovich, K.: Enumeration of $$2$$-level polytopes. Math. Program. Comput. 11(1), 173\u2013210 (2019)","journal-title":"Math. Program. Comput."},{"issue":"10","key":"347_CR4","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":"3","key":"347_CR5","doi-asserted-by":"publisher","first-page":"1637","DOI":"10.1137\/18M1233649","volume":"33","author":"J Gouveia","year":"2019","unstructured":"Gouveia, J., Macchia, A., Thomas, R.R., Wiebe, A.: The slack realization space of a polytope. SIAM J. Discrete Math. 33(3), 1637\u20131653 (2019)","journal-title":"SIAM J. Discrete Math."},{"key":"347_CR6","doi-asserted-by":"crossref","unstructured":"Gouveia, J., Macchia, A., Thomas, R.R., Wiebe, A.: Projectively unique polytopes and toric slack ideals. J. Pure Appl. Algebra 224(5), #\u00a0106229 (2020)","DOI":"10.1016\/j.jpaa.2019.106229"},{"key":"347_CR7","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"},{"key":"347_CR8","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0019-9","volume-title":"Convex Polytopes","author":"B Gr\u00fcnbaum","year":"2003","unstructured":"Gr\u00fcnbaum, B.: Convex Polytopes. Graduate Texts in Mathematics, vol. 221. Springer, New York (2003)"},{"key":"347_CR9","doi-asserted-by":"crossref","unstructured":"Macchia, A., Wiebe, A.: Slack ideals in Macaulay2 (2020). arXiv:2003.07382","DOI":"10.1007\/978-3-030-52200-1_22"},{"issue":"4","key":"347_CR10","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/0012-365X(76)90067-4","volume":"14","author":"P McMullen","year":"1976","unstructured":"McMullen, P.: Constructions for projectively unique polytopes. Discrete Math. 14(4), 347\u2013358 (1976)","journal-title":"Discrete Math."},{"issue":"3","key":"347_CR11","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/BF00181326","volume":"3","author":"MA Perles","year":"1974","unstructured":"Perles, M.A., Shephard, G.C.: A construction for projectively unique polytopes. Geometriae Dedicata 3(3), 357\u2013363 (1974)","journal-title":"Geometriae Dedicata"},{"key":"347_CR12","doi-asserted-by":"crossref","unstructured":"Richter-Gebert, J.: Realization Spaces of Polytopes. Lecture Notes in Mathematics, vol. 1643. Springer, Berlin (1996)","DOI":"10.1007\/BFb0093761"},{"issue":"1","key":"347_CR13","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."},{"key":"347_CR14","unstructured":"Stanley, R.P.: Enumerative Combinatorics. Vol.\u00a01. Cambridge Studies in Advanced Mathematics, vol.\u00a049. Cambridge University Press, Cambridge (2012)"},{"key":"347_CR15","unstructured":"Steinitz, E.: Polyeder und Raumeinteilungen. In: Encyklop\u00e4die der Mathematischen Wissenschaften, vol. 3-1-2, #\u00a012 (1922)"},{"issue":"12","key":"347_CR16","doi-asserted-by":"publisher","first-page":"5071","DOI":"10.1090\/proc\/14630","volume":"147","author":"I Swanson","year":"2019","unstructured":"Swanson, I., Walker, R.M.: Tensor-multinomial sums of ideals: primary decompositions and persistence of associated primes. Proc. Am. Math. Soc. 147(12), 5071\u20135082 (2019)","journal-title":"Proc. Am. Math. Soc."},{"key":"347_CR17","unstructured":"Wiebe, A.: Realization Spaces of Polytopes and Matroids. PhD thesis, University of Washington (2019)"},{"key":"347_CR18","doi-asserted-by":"crossref","unstructured":"Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer, New York (1995)","DOI":"10.1007\/978-1-4613-8431-1"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-021-00347-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-021-00347-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-021-00347-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,5]],"date-time":"2022-02-05T22:13:31Z","timestamp":1644099211000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-021-00347-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,1]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["347"],"URL":"https:\/\/doi.org\/10.1007\/s00454-021-00347-8","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2021,12,1]]},"assertion":[{"value":"3 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 July 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 December 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}