On the number of small Steiner triple systems with Veblen points
Combinatorics
2025-01-09 v2 Group Theory
Abstract
The concept of Schreier extensions of loops was introduced in the general case in [11] and, more recently, it has been explored in the context of Steiner loops in [6]. In the latter case, it gives a powerful method for constructing Steiner triple systems containing Veblen points. Counting all Steiner triple systems of order v is an open problem for v>21. In this paper, we investigate the number of Steiner triple systems of order 19, 27 and 31 containing Veblen points and we present some examples.
Cite
@article{arxiv.2411.16307,
title = {On the number of small Steiner triple systems with Veblen points},
author = {Mario Galici and Giuseppe Filippone},
journal= {arXiv preprint arXiv:2411.16307},
year = {2025}
}