1 citations · 2 across the 8 of their papers we have counts for
12 papers
Constructions of Sarvate-Beam Group Divisible Designs
Peter J. Dukes, Joanna Niezen
A balanced incomplete block design is a set system in which all pairs of distinct elements occur with a constant frequency. By contrast, a Sarvate-Beam design induces an interval o…
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…
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.
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…
Local Balance in Graph Decompositions
Flora C. Bowditch, Peter J. Dukes
In a balanced graph decomposition, every vertex of the host graph appears in the same number of blocks. We propose the use of colored loops as a framework for unifying various othe…
On the Algebraic Combinatorics of Injections and its Applications to Injection Codes
Peter J. Dukes, Ferdinand Ihringer, Nathan Lindzey
We consider the algebraic combinatorics of the set of injections from a -element set to an -element set. In particular, we give a new combinatorial formula for the spherical…