On the Wilson monoid of a pairwise balanced design

Stuart Margolis, John Rhodes, Pedro V. Silva

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)637-665
Number of pages29
JournalAlgebraic Combinatorics
Issue number3
StatePublished - 2020

Bibliographical note

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  • Boolean representable simplicial complex
  • Matroid
  • Pairwise balanced design
  • Truncation
  • Wilson monoid


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