Professor, Director of Graduate Programs
Professor; Ph.D., Oxford University, 1988. Combinatorics.
- Designs and other combinatorial structures: designs and arrays, single-change circular covering designs, sequential covering designs, orthogonal arrays, properly separated permutations, and Latin squares; have invented a board game called squares. Designs are used worldwide by agricultural scientists when testing new fertilizers, pharmaceutical companies in testing new drugs, and sports organizations for arranging game schedules, etc.
- Graph theory: enumeration, coloring, graph sequences and digraphs, magic labelings, injections, neighborhood properties. Graphs are used by chemists, the business community, telecommunications companies, etc., to model chemical structures, small economies, telephone networks, etc. Any advance in the theory of graphs has potential benefits for these people.
- Combinatorial interpretations of polynomials: Bessel polynomials and derivatives, Lommel polynomials and derivatives, multivariate matchings polynomials of graphs, m-path cover polynomials of graphs, vertex/matching-partition function of graphs.
- Rhombic tilings of (n,k)-ovals, (n,k,λ)-cyclic difference sets, and related topics, with A. Schoen. Discrete Mathematics 313 (2013), pp. 129-154.
- Zeons, permanents, the Johnson scheme, and generalised derangements, with P. Feinsilver. International Journal of Combinatorics, (2011), v.2011, Article ID 539030, 29 pages.
- On k-minimum and m-minimum Edge Magic Injections of Graphs. with J. Trono. Discrete Mathematics.(2010) v.310 (no.1) pp.56–69
- Multivariate Matching Polynomials of Cyclically Labelled Graphs, with P. Feinsilver. Discrete Mathematics. (2009) v.309 pp.3205–3218
- Constructing and Classifying Neighborhood anti-Sperner Graphs, Discrete Mathematics (2008) v.308 (no.23) pp.5428–5445.
- Double Arrays, Triple Arrays, and Balanced Grids, with N. Phillips, J. Yucas, W. Wallis. Designs, Codes, and Cryptography.(2005) v.35 pp.21–45.
- Generating Sequences of Clique-Symmetric Graphs via Eulerian Digraphs, with T. Porter. Discrete Mathematics(2004) v.287 pp.85–91.
- Single-change Circular Covering Designs. Discrete Mathematics (1999) v.197/8 pp.561–588.
- Counting Structures in the M¨obius Ladder. Discrete Mathematics (1998) v.184 pp.137–164.