3 papers
math.CO2024
Duplicated Steiner triple systems with self-orthogonal near resolutions
Peter J. Dukes, Esther R. Lamken
A Steiner triple system, STS, is a family of -subsets (blocks) of a set of elements such that any two elements occur together in precisely one block. A collection of tr…
math.CO2021
An Update on the Existence of Kirkman Triple Systems with Subdesigns
Peter Dukes, Esther Lamken
A Kirkman triple system of order , KTS, is a resolvable Steiner triple system on elements. In this paper, we investigate an open problem posed by Doug Stinson, namely t…
math.CO2018
Constructions and uses of incomplete pairwise balanced designs
Peter J. Dukes, Esther R. Lamken
We give explicit constructions for incomplete pairwise balanced designs IPBD, or, equivalently, edge-decompositions of a difference of two cliques in…