An Upper bound on the number of Steiner triple systems

Details An Upper bound on the number of Steiner triple systems An Upper bound on the number of Steiner triple systems

2011-08-25

arxiv.org/abs/1108.5042v3

Mathematics

Combinatorics

13 pages

Scientific paper

Let STS(n) denote the number of Steiner triple systems on n vertices, and let F(n) denote the number of 1-factorizations of the complete graph on n vertices. We prove the following upper bound. STS(n) <= ((1 + o(1)) (n/e^2))^(n^2/6) F(n) <= ((1 + o(1)) (n/e^2))^(n^2/2) We conjecture that the bound is sharp. Our main tool is the entropy method.

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