High-girth Steiner triple systems

From To appear in forthcoming issues by Matthew Kwan, Ashwin Sah, Mehtaab Sawhney, Michael Simkin

Abstract

We prove a 1973 conjecture due to Erdős on the existence of Steiner triple systems with arbitrarily high girth.

Keywords
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Mathematical Subject Classification

Primary 2020:

Milestones
Received: 14 January 2022
Revised: 23 January 2024
Accepted: 30 April 2024

Authors

Matthew Kwan

Institute of Science and Technology Austria (IST Austria), 3400 Klosterneuburg, Austria

Ashwin Sah

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

Mehtaab Sawhney

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

Michael Simkin

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA