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.
Filippone Giuseppe, Galici Mario (2025). On the number of small Steiner triple systems with Veblen points. DISCRETE MATHEMATICS, 348(1) [10.1016/j.disc.2024.114294].
On the number of small Steiner triple systems with Veblen points
Filippone GiuseppeSoftware
;Galici Mario
Conceptualization
2025-01-01
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.
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