4 citations · 11 across the 23 of their papers we have counts for
5 papers · 1 filter
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…
On the minimum degree required for a triangle decomposition
Peter J. Dukes, Daniel Horsley
We prove that, for sufficiently large , every graph of order with minimum degree at least has a fractional edge-decomposition into triangles. We do this by refining…
Some new block designs of dimension three
Coen del Valle, Peter J. Dukes
The dimension of a block design is the maximum positive integer such that any of its points are contained in a proper subdesign. Pairwise balanced designs PBD have d…
Leaves for packings with block size four
Yanxun Chang, Peter J. Dukes, Tao Feng
We consider maximum packings of edge-disjoint -cliques in the complete graph . When or , these are simply block designs. In other congruence class…
A lower bound on permutation codes of distance
Sergey Bereg, Peter Dukes
A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length and minimum distance…