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.

Recent publications:

  • The linear system for Sudoku and a fractional completion threshold (with K. Nimegeers)
  • Six permutation patterns force quasirandomness (with G. Crudele and J.A. Noel)
  • Families of modular arithmetic progressions with an interval of distance multiplicities (with T. Gaede)
  • Extremal bounds for three-neighbour bootstrap percolation in dimensions two and three (with J.A. Noel and A.E. Romer)
  • 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:

  • Search for short quasirandom-forcing linear combinations of permutations
  • 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


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