{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:38:10Z","timestamp":1776728290610,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"238","license":[{"start":{"date-parts":[[2002,11,21]],"date-time":"2002-11-21T00:00:00Z","timestamp":1037836800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes\n all<\/italic>\n KTS(21)s having a nontrivial automorphism group. None of these is doubly resolvable. Four are quadrilateral-free, providing the first examples of such a KTS(21).\n <\/p>","DOI":"10.1090\/s0025-5718-01-01372-2","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"873-881","source":"Crossref","is-referenced-by-count":10,"title":["Kirkman triple systems of order 21 with nontrivial automorphism group"],"prefix":"10.1090","volume":"71","author":[{"given":"Myra","family":"Cohen","sequence":"first","affiliation":[]},{"given":"Charles","family":"Colbourn","sequence":"additional","affiliation":[]},{"given":"Lee","family":"Ives","sequence":"additional","affiliation":[]},{"given":"Alan","family":"Ling","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,11,21]]},"reference":[{"issue":"1-2","key":"1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0166-218X(99)00228-0","article-title":"Asymptotically optimal erasure-resilient codes for large disk arrays","volume":"102","author":"Chee, Yeow Meng","year":"2000","journal-title":"Discrete Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0166-218X","issn-type":"print"},{"key":"2","unstructured":"C.J. Colbourn, E.R. Lamken, A.C.H. Ling, and W.H. Mills, The existence of Kirkman squares \u2013 doubly resolvable (\ud835\udc63,3,1)-BIBDs, Designs Codes Crypt., to appear."},{"key":"3","doi-asserted-by":"crossref","unstructured":"C.J. Colbourn and A. Rosa, Triple Systems, Oxford University Press, 1999.","DOI":"10.1093\/oso\/9780198535768.001.0001"},{"key":"4","first-page":"97","article-title":"A completion conjecture for Kirkman triple systems","volume":"50","author":"Dejter, I. J.","year":"1996","journal-title":"Utilitas Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0315-3681","issn-type":"print"},{"key":"5","unstructured":"P.B. Gibbons, Computational methods in design theory, in CRC Handbook of Combinatorial Designs, (C.J. Colbourn and J.H. Dinitz, editors), CRC Press, Boca Raton FL, 1996, pp. 718\u2013740."},{"key":"6","unstructured":"T.P. Kirkman, Note on an unanswered prize question, Cambridge and Dublin Math. J. 5 (1850), 255-262."},{"issue":"155","key":"7","doi-asserted-by":"publisher","first-page":"209","DOI":"10.2307\/2007514","article-title":"A class of Steiner triple systems of order 21 and associated Kirkman systems","volume":"37","author":"Mathon, Rudolf A.","year":"1981","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"8","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1002\/net.3230130407","article-title":"Dynamic matchings and quasidynamic fractional matchings. I, II","volume":"13","author":"Orlin, James B.","year":"1983","journal-title":"Networks","ISSN":"https:\/\/id.crossref.org\/issn\/0028-3045","issn-type":"print"},{"key":"9","unstructured":"B. D. McKay, Nauty Users Guide (Version 1.5), Technical Report TR-CS-90-02, 1990 Computer Science Department, Australian National University."},{"key":"10","first-page":"187","article-title":"Solution of Kirkman\u2019s schoolgirl problem","author":"Ray-Chaudhuri, D. K.","year":"1971"},{"key":"11","first-page":"93","article-title":"Steiner triple systems of order 21 with automorphisms of order 7","volume":"23","author":"Tonchev, Vladimir D.","year":"1987","journal-title":"Ars Combin.","ISSN":"https:\/\/id.crossref.org\/issn\/0381-7032","issn-type":"print"},{"key":"12","doi-asserted-by":"crossref","unstructured":"W.S.B. Woolhouse, On triadic combinations of 15 symbols, Lady\u2019s and Gentleman\u2019s Diary (1862) 84\u201388. Reprinted in Assurance Magazine 10, 275\u2013281.","DOI":"10.1017\/S2046165800002203"},{"key":"13","unstructured":"W.S.B. Woolhouse, On triadic combinations, Lady\u2019s and Gentleman\u2019s Diary (1863), 79\u201390."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01372-2\/S0025-5718-01-01372-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01372-2\/S0025-5718-01-01372-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:56:59Z","timestamp":1776725819000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01372-2\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11,21]]},"references-count":13,"journal-issue":{"issue":"238","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["S0025-5718-01-01372-2"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-01-01372-2","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2001,11,21]]}}}