Research

I love interesting mathematics in many areas, but my research focus is combinatorics. A common theme is applying algebraic or analytic methods to combinatorial problems, especially where extremal or balanced structures are involved.

Some publications:

  • Balancing permuted copies of multigraphs and integer matrices (with C. del Valle)
  • Number cubes with consecutive line sums (with J. Niezen)
  • Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields (with X. Martínez-Rivera)
  • On the algebraic combinatorics of injections and its applications to injection codes (with F. Ihringer and N. Lindzey)
  • other articles on MathReviews (library credentials required)
  • my thesis, sort of; in this, a standalone chapter was deleted and some updates on the main theme were added

    Code/data files:

  • Matrix balancing calculator
  • Triangle decomposition game (android): triangle-wiper.apk
  • Possibly complete list of facets of the cone of 9-vertex weighted graphs generated by triangles: facets-tri9.txt
  • Small latin square intersections: int-ls-data.gz
  • Destructing tight designs with small 'beta': tightsearch.c

    Conferences/Workshops:

  • I am a co-organizer of Stinson 66, a conference on mathematics influenced by Doug Stinson.