An Upper bound on the number of Steiner triple systems
Combinatorics
2011-10-13 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1108.5042,
title = {An Upper bound on the number of Steiner triple systems},
author = {Nathan Linial and Zur Luria},
journal= {arXiv preprint arXiv:1108.5042},
year = {2011}
}
Comments
13 pages