On the Wilson Monoid of a Pairwise Balanced Design
Combinatorics
2019-04-09 v1 Group Theory
Abstract
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 elements
Keywords
Cite
@article{arxiv.1904.03840,
title = {On the Wilson Monoid of a Pairwise Balanced Design},
author = {Stuart W. Margolis and John Rhodes and Pedro Silva},
journal= {arXiv preprint arXiv:1904.03840},
year = {2019}
}