{"abstract":[{"lang":"eng","text":"We show that for any  𝑛  divisible by 3, almost all order-  𝑛  Steiner triple systems have a perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of perfect matchings in a Steiner triple system and show that almost all Steiner triple systems essentially attain this maximum. We accomplish this via a general theorem comparing a uniformly random Steiner triple system to the outcome of the triangle removal process, which we hope will be useful for other problems. Our methods can also be adapted to other types of designs; for example, we sketch a proof of the theorem that almost all Latin squares have transversals."}],"publication_status":"published","publication":"Proceedings of the London Mathematical Society","author":[{"last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567"}],"doi":"10.1112/plms.12373","_id":"9581","publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"type":"journal_article","extern":"1","volume":121,"date_updated":"2023-02-23T14:01:43Z","oa":1,"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","external_id":{"arxiv":["1611.02246"]},"page":"1468-1495","status":"public","date_created":"2021-06-22T06:35:16Z","month":"12","citation":{"mla":"Kwan, Matthew Alan. “Almost All Steiner Triple Systems Have Perfect Matchings.” <i>Proceedings of the London Mathematical Society</i>, vol. 121, no. 6, Wiley, 2020, pp. 1468–95, doi:<a href=\"https://doi.org/10.1112/plms.12373\">10.1112/plms.12373</a>.","ama":"Kwan MA. Almost all Steiner triple systems have perfect matchings. <i>Proceedings of the London Mathematical Society</i>. 2020;121(6):1468-1495. doi:<a href=\"https://doi.org/10.1112/plms.12373\">10.1112/plms.12373</a>","short":"M.A. Kwan, Proceedings of the London Mathematical Society 121 (2020) 1468–1495.","ieee":"M. A. Kwan, “Almost all Steiner triple systems have perfect matchings,” <i>Proceedings of the London Mathematical Society</i>, vol. 121, no. 6. Wiley, pp. 1468–1495, 2020.","chicago":"Kwan, Matthew Alan. “Almost All Steiner Triple Systems Have Perfect Matchings.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2020. <a href=\"https://doi.org/10.1112/plms.12373\">https://doi.org/10.1112/plms.12373</a>.","ista":"Kwan MA. 2020. Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. 121(6), 1468–1495.","apa":"Kwan, M. A. (2020). Almost all Steiner triple systems have perfect matchings. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.12373\">https://doi.org/10.1112/plms.12373</a>"},"article_processing_charge":"No","oa_version":"Preprint","issue":"6","title":"Almost all Steiner triple systems have perfect matchings","quality_controlled":"1","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1611.02246","open_access":"1"}],"language":[{"iso":"eng"}],"intvolume":"       121","date_published":"2020-12-01T00:00:00Z","day":"01","year":"2020","publisher":"Wiley","article_type":"original"}