4 citations · 11 across the 23 of their papers we have counts for
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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.CO2021
Number cubes with consecutive line sums
Peter Dukes, Joanna Niezen
We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
math.CO2021
Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields
Peter J. Dukes, Xavier Martínez-Rivera
The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix is defined as , where $\ell_j…