An upper bound on the number of Steiner triple systems

Nathan Linial, Zur Luria*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)399-406
Number of pages8
JournalRandom Structures and Algorithms
Volume43
Issue number4
DOIs
StatePublished - Dec 2013

Keywords

  • Asymptotics
  • Combinatorial enumeration
  • Steiner triple systems
  • The entropy method

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