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• W3100797722 abstract "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." @default.
• W3100797722 created "2020-11-23" @default.
• W3100797722 creator A5064348920 @default.
• W3100797722 date "2020-07-21" @default.
• W3100797722 modified "2023-10-10" @default.
• W3100797722 title "Almost all Steiner triple systems have perfect matchings" @default.
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• W3100797722 doi "https://doi.org/10.1112/plms.12373" @default.
• W3100797722 hasPublicationYear "2020" @default.
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