Oriented Steiner Triple Systems, Steiner Products, and Dynamics
Jake Kettinger, Chris Peterson
TL;DR
This paper explores oriented Steiner triple systems, introduces Steiner products resembling cross products, classifies systems for sizes 7 and 9, and studies their dynamic properties.
Contribution
It classifies oriented Steiner triple systems for sizes 7 and 9 and investigates the dynamics of their associated Steiner products.
Findings
Classified oriented Steiner triple systems on 7 and 9 elements.
Defined a Steiner product resembling the cross product.
Analyzed the dynamics of Steiner products.
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.
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