Oriented Steiner Triple Systems, Steiner Products, and Dynamics
Combinatorics
2025-07-15 v1 Rings and Algebras
Abstract
Let S denote a Steiner triple system on an n-element set. An orientation of S is an assignment of a cyclic ordering to each of the triples in S. From an oriented Steiner triple system, one can define an anticommutative bilinear operation on Rn resembling the cross product. We call this bilinear operation a Steiner product. We classify the oriented Steiner triple systems on sets of size 7 and 9 and investigate the dynamics of their associated Steiner products.
Cite
@article{arxiv.2507.09396,
title = {Oriented Steiner Triple Systems, Steiner Products, and Dynamics},
author = {Jake Kettinger and Chris Peterson},
journal= {arXiv preprint arXiv:2507.09396},
year = {2025}
}
Comments
24 pages, 2 figures