Year: 2011
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Linial, Nathan, Luria, Zur
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
OpenAlex ID: W2951782391