John McSorley SIUC, Mathematics Associate Professor   Ph.D. Oxford University, 1988   Combinatorics   Office: Neckers A 383 Office Phone: 618-453-6596 Email: jmcsorley at math.siu.edu Web Page: www.math.siu.edu/jmcsorley Home Page: www.math.siu.edu/mcsorley/McS-publications.html

Research Interests

1.  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.
2.  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.
3.  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.

Selected Publications

1. Complete enumeration and properties of binary pseudo-Youden designs PYD(9,6,6), with N.C.K. Phillips, Journal of Statistical Planning and Inference 137 (2007), 1464-1473.
2. Double arrays, triple arrays, and balanced grids, with N.C.K. Phillips, J. Yucas, W.D. Wallis, Designs, Codes, and Cryptography 35 (2005), 21-45.
3. Generating sequences of clique symmetric graphs via Eulerian digraphs, with T. Porter, Discrete Mathematics 287 (2004), 85-91.
4. Single-change circular covering designs, Discrete Mathematics 197/8 (1999), 561-588.
5. Counting structures in the Mobius ladder, Discrete Mathematics 184 (1998), 137-164.