## 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.

#### 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. MartÃnez-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

#### Conferences/Workshops:

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