An upper bound on the number of Steiner triple systems

Nathan Linial; Zur Luria

doi:10.1002/rsa.20487

An upper bound on the number of Steiner triple systems

Nathan Linial, Zur Luria^*

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

Richard Wilson conjectured in 1974 the following asymptotic formula for the number of n -vertex Steiner triple systems: Our main result is that The proof is based on the entropy method. As a prelude to this proof we consider the number F(n) of 1 -factorizations of the complete graph on n vertices. Using the Kahn-Lovász theorem it can be shown that We show how to derive this bound using the entropy method. Both bounds are conjectured to be sharp.

Original language	English
Pages (from-to)	399-406
Number of pages	8
Journal	Random Structures and Algorithms
Volume	43
Issue number	4
DOIs	https://doi.org/10.1002/rsa.20487
State	Published - Dec 2013

Keywords

Asymptotics
Combinatorial enumeration
Steiner triple systems
The entropy method

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10.1002/rsa.20487

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An upper bound on the number of Steiner triple systems

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Keywords

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