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Some complementary Gray codes
Adam Hoyt, Brett Stevens
A complementary Gray code for binary n-tuples is one that, when all the tuples are complemented, is identical to itself; this is equivalent to the complement of the first half of t…
Sets of mutually orthogoval projective and affine planes
Charles J. Colbourn, Colin Ingalls, Jonathan Jedwab +3
A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at…
An Extension of the Erdős-Ko-Rado Theorem to uniform set partitions
Karen Meagher, Mahsa N. Shirazi, Brett Stevens
A -partition is a set partition which has blocks each of size . Two uniform set partitions and are said to be partially -intersecting if there exist…
The combinatorial game nofil played on Steiner Triple Systems
Melissa A. Huggan, Svenja Huntemann, Brett Stevens
We introduce an impartial combinatorial game on Steiner triple systems called Nofil. Players move alternately, choosing points of the triple system. If a player is forced to fill a…
Non-uniform covering array with symmetric forbidden edge constraints
Brett Stevens
It has been conjectured that whenever an optimal covering array exists there is also a uniform covering array with the same parameters and this is true for all known optimal coveri…
Upper bounds on the sizes of variable strength covering arrays using the Lovász local lemma
Lucia Moura, Sebastian Raaphorst, Brett Stevens
Covering arrays are generalizations of orthogonal arrays that have been widely studied and are used in software testing. The probabilistic method has been employed to derive upper…