2 research outputs found
The Steiner triple systems of order 21 with a transversal subdesign TD(3,6)
We prove several structural properties of Steiner triple systems (STS) of
order 3w+3 that include one or more transversal subdesigns TD(3,w). Using an
exhaustive search, we find that there are 2004720 isomorphism classes of
STS(21) including a subdesign TD(3,6), or, equivalently, a 6-by-6 latin square
On the Wilson Monoid of a Pairwise Balanced Design
We give a new perspective of the relationship between simple matroids of rank
3 and pairwise balanced designs, connecting Wilson's theorems and tools with
the theory of truncated boolean representable simplicial complexes. We also
introduce the concept of Wilson monoid W(X) of a pairwise balanced design X. We
present some general algebraic properties and study in detail the cases of
Steiner triple systems up to 19 points, as well as the case where a single
block has more than 2 element