{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T15:54:04Z","timestamp":1758815644748},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,5,4]],"date-time":"2020-05-04T00:00:00Z","timestamp":1588550400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,5,4]],"date-time":"2020-05-04T00:00:00Z","timestamp":1588550400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s10898-020-00908-w","type":"journal-article","created":{"date-parts":[[2020,5,4]],"date-time":"2020-05-04T02:02:22Z","timestamp":1588557742000},"page":"261-268","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Using symbolic calculations to determine largest small polygons"],"prefix":"10.1007","volume":"81","author":[{"given":"Charles","family":"Audet","sequence":"first","affiliation":[]},{"given":"Pierre","family":"Hansen","sequence":"additional","affiliation":[]},{"given":"Dragutin","family":"Svrtan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,5,4]]},"reference":[{"issue":"2","key":"908_CR1","doi-asserted-by":"publisher","first-page":"175","DOI":"10.4169\/amer.math.monthly.124.2.175","volume":"124","author":"C Audet","year":"2017","unstructured":"Audet, C.: Maximal area of equilateral small polygons. Am. Math. Monthly 124(2), 175\u2013178 (2017)","journal-title":"Am. Math. Monthly"},{"issue":"2","key":"908_CR2","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s10898-006-9065-5","volume":"38","author":"C Audet","year":"2007","unstructured":"Audet, C., Hansen, P., Messine, F.: Extremal problems for convex polygons. J. Global Optim. 38(2), 163\u2013179 (2007)","journal-title":"J. Global Optim."},{"key":"908_CR3","first-page":"1","volume-title":"Lectures on Global Optimization, Volume 55 of Fields Institute Communications","author":"C Audet","year":"2009","unstructured":"Audet, C., Hansen, P., Messine, F.: Extremal problems for convex polygons\u2014an update. In: Pardalos, P.M., Coleman, T.F. (eds.) Lectures on Global Optimization, Volume 55 of Fields Institute Communications, pp. 1\u201316. American Mathematical Society, Providence (2009)"},{"key":"908_CR4","unstructured":"Audet, C., Hansen, P., Messine, F.: Ranking small regular polygons by area and by perimeter. J. Appl. Ind. Math. 3(1), 21\u201327 (2009). Original Russian text: Diskretnyi Analiz i Issledovanie Operatsii, 15(3), 65\u201373 (2008)"},{"issue":"1","key":"908_CR5","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1006\/jcta.2001.3225","volume":"98","author":"C Audet","year":"2002","unstructured":"Audet, C., Hansen, P., Messine, F., Xiong, J.: The largest small octagon. J. Comb. Theory Appl. Ser. A 98(1), 46\u201359 (2002)","journal-title":"J. Comb. Theory Appl. Ser. A"},{"issue":"3","key":"908_CR6","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1080\/10586458.2000.10504419","volume":"9","author":"P Borwein","year":"2000","unstructured":"Borwein, P., Mossinghoff, M.J.: Polynomials with height 1 and prescribed vanishing at 1. Exp. Math. 9(3), 425\u2013433 (2000)","journal-title":"Exp. Math."},{"key":"908_CR7","volume-title":"Introduction to the Geometry of Complex Numbers","author":"R Deaux","year":"1954","unstructured":"Deaux, R.: Introduction to the Geometry of Complex Numbers. Ungar, New York (1954)"},{"issue":"8","key":"908_CR8","doi-asserted-by":"publisher","first-page":"1515","DOI":"10.1016\/j.jcta.2007.02.006","volume":"114","author":"J Foster","year":"2007","unstructured":"Foster, J., Szabo, T.: Diameter graphs of polygons and the proof of a conjecture of Graham. J. Combin. Theory Ser. A 114(8), 1515\u20131525 (2007)","journal-title":"J. Combin. Theory Ser. A"},{"key":"908_CR9","volume-title":"Discriminants, Resultants, and Multidimensional Determinants","author":"IM Gelfand","year":"2009","unstructured":"Gelfand, I.M., Kapranov, M.M., Zelevinsky, A.V.: Discriminants, Resultants, and Multidimensional Determinants. Birkh\u00e4user, Boston (2009)"},{"key":"908_CR10","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/0097-3165(75)90004-7","volume":"18","author":"RL Graham","year":"1975","unstructured":"Graham, R.L.: The largest small hexagon. J. Combin. Theory 18, 165\u2013170 (1975)","journal-title":"J. Combin. Theory"},{"issue":"3","key":"908_CR11","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1007\/s10898-011-9818-7","volume":"56","author":"D Henrion","year":"2013","unstructured":"Henrion, D., Messine, F.: Finding largest small polygons with GloptiPoly. J. Global Optim. 56(3), 1017\u20131028 (2013)","journal-title":"J. Global Optim."},{"issue":"1","key":"908_CR12","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1145\/1086823.1086825","volume":"8","author":"SC Johnson","year":"1974","unstructured":"Johnson, S.C., Graham, R.L.: Problem #7. SIGSAM Bull. 8(1), 4\u20134 (1974)","journal-title":"SIGSAM Bull."},{"issue":"2","key":"908_CR13","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1145\/1089220.1089224","volume":"14","author":"D Lazard","year":"1980","unstructured":"Lazard, D.: Problem 7 and systems of algebraic equations. SIGSAM Bull. 14(2), 26\u201329 (1980)","journal-title":"SIGSAM Bull."},{"issue":"2","key":"908_CR14","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s00454-006-1238-y","volume":"36","author":"MJ Mossinghoff","year":"2006","unstructured":"Mossinghoff, M.J.: Isodiametric problems for polygons. Discrete Comput. Geom. 36(2), 363\u2013379 (2006)","journal-title":"Discrete Comput. Geom."},{"key":"908_CR15","first-page":"251","volume":"31","author":"K Reinhardt","year":"1922","unstructured":"Reinhardt, K.: Extremale polygone gegebenen durchmessers. Jahresber. Deutsch. Math. Verein 31, 251\u2013270 (1922)","journal-title":"Jahresber. Deutsch. Math. Verein"},{"key":"908_CR16","unstructured":"Yuan, B.: The largest small hexagon. Master\u2019s Thesis, Department of Mathematics, National University of Singapore, (2004)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00908-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-020-00908-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00908-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,12]],"date-time":"2021-08-12T06:08:29Z","timestamp":1628748509000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-020-00908-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,4]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["908"],"URL":"https:\/\/doi.org\/10.1007\/s10898-020-00908-w","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,4]]},"assertion":[{"value":"2 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}