{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T05:56:07Z","timestamp":1768974967006,"version":"3.49.0"},"reference-count":20,"publisher":"Informa UK Limited","issue":"7","license":[{"start":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T00:00:00Z","timestamp":1715558400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["The American Mathematical Monthly"],"published-print":{"date-parts":[[2024,8,8]]},"DOI":"10.1080\/00029890.2024.2345576","type":"journal-article","created":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T11:17:30Z","timestamp":1715599050000},"page":"595-607","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":0,"title":["Building Sets of Permutation-Fair Dice"],"prefix":"10.1080","volume":"131","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6758-8027","authenticated-orcid":false,"given":"Michael","family":"Purcell","sequence":"first","affiliation":[{"name":"School of Computing, The Australian National University","place":["Canberra, Australia"]}]}],"member":"301","published-online":{"date-parts":[[2024,5,13]]},"reference":[{"key":"e_1_3_3_2_1","unstructured":"Harshbarger E. Go first dice; 2023. Website. Available from: http:\/\/www.ericharshbarger.org\/dice\/go_first_dice.html."},{"key":"e_1_3_3_3_1","unstructured":"Polylog. We designed special dice using math but there\u2019s a catch; 2022. YouTube. Available from: https:\/\/www.youtube.com\/watch?v=-64UT8yikng&t=66s"},{"key":"e_1_3_3_4_1","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.6522795"},{"key":"e_1_3_3_5_1","unstructured":"Dunning I Mitchell S O\u2019Sullivan M. PuLP: A linear programming toolkit for Python; 2011."},{"key":"e_1_3_3_6_1","doi-asserted-by":"publisher","DOI":"10.2478\/rmm-2023-0004"},{"key":"e_1_3_3_7_1","unstructured":"Harshbarger E. A method to construct n\u2009+\u20091-player permutation-fair sets of dice from known n-player permutation fair sets; 2018."},{"key":"e_1_3_3_8_1","first-page":"67","article-title":"On a paradox in applied probabilities","volume":"7","author":"Steinhaus H","year":"1959","unstructured":"Steinhaus H, Trybu\u0142a S. On a paradox in applied probabilities. Bull Pol Acad Sci Math. 1959;7:67\u201369.","journal-title":"Bull Pol Acad Sci Math"},{"key":"e_1_3_3_9_1","first-page":"321","article-title":"On the paradox of three random variables","volume":"5","author":"Trybu\u0142a S.","year":"1961","unstructured":"Trybu\u0142a S. On the paradox of three random variables. Zastos Mat. 1961;5:321\u2013332.","journal-title":"Zastos Mat"},{"key":"e_1_3_3_10_1","first-page":"143","article-title":"On the paradox of n random variables","volume":"8","author":"Trybu\u0142a S.","year":"1965","unstructured":"Trybu\u0142a S. On the paradox of n random variables. Zastos Mat. 1965;8:143\u2013156.","journal-title":"Zastos Mat"},{"key":"e_1_3_3_11_1","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican1270-110"},{"key":"e_1_3_3_12_1","first-page":"241","article-title":"Tied dice. II. Some asymptotic results","volume":"90","author":"Cooley C","year":"2014","unstructured":"Cooley C, Ella W, Follett M, Gilson E, Traldi L. Tied dice. II. Some asymptotic results. J Combin Math Combin Comput. 2014;90:241\u2013248.","journal-title":"J Combin Math Combin Comput"},{"key":"e_1_3_3_13_1","first-page":"85","article-title":"Tied dice","volume":"68","author":"Kronenthal BG","year":"2009","unstructured":"Kronenthal BG, Traldi L. Tied dice. J Combin Math Combin Comput. 2009;68:85\u201396.","journal-title":"J Combin Math Combin Comput"},{"key":"e_1_3_3_14_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1706.08986"},{"key":"e_1_3_3_15_1","doi-asserted-by":"publisher","DOI":"10.4169\/college.math.j.48.1.10"},{"key":"e_1_3_3_16_1","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/6648248"},{"key":"e_1_3_3_17_1","doi-asserted-by":"publisher","DOI":"10.4169\/college.math.j.48.1.2"},{"key":"e_1_3_3_18_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2018.1427392"},{"key":"e_1_3_3_19_1","doi-asserted-by":"publisher","DOI":"10.2307\/2324089"},{"key":"e_1_3_3_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5648-9_4"},{"key":"e_1_3_3_21_1","unstructured":"Polymath 13. The probability that a random triple of dice is transitive. Website. 2017. Available from: https:\/\/polymathprojects.org."}],"container-title":["The American Mathematical Monthly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/00029890.2024.2345576","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T16:41:17Z","timestamp":1768927277000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/00029890.2024.2345576"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,13]]},"references-count":20,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2024,8,8]]}},"alternative-id":["10.1080\/00029890.2024.2345576"],"URL":"https:\/\/doi.org\/10.1080\/00029890.2024.2345576","relation":{},"ISSN":["0002-9890","1930-0972"],"issn-type":[{"value":"0002-9890","type":"print"},{"value":"1930-0972","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,13]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=uamm20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=uamm20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2023-02-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-10-03","order":1,"name":"revised","label":"Revised","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-10-04","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-05-13","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}