Publications
 
The First Nontrivial HalesJewett Number is Four 
With Neil Hindman. Ars Combinatoria 113 (2014), 385390.
We prove that the HalesJewett number \(HJ(3,2)\) is 4; that is,
if the length 4 words over the alphabet \(\{1,2,3\}\) are 2colored, there must
exist a monochromatic combinatorial line. Some lower bounds are also
stated; the proofs of these are not included in the paper, but they
can be found here.

5PM: Secure Pattern Matching 
With Josh Baron, Karim El Defrawy, Kirill Minkovich, and Rafail Ostrovsky. In proceedings of the 8th conference on Security and Cryptography for Networks (SCN) (2012),
and the SCN 2012 special issue of Journal of Computer Security.
We present a new secure pattern matching scheme that employs fully homomorphic encryption. This allows searches to be performed without revealing the search
pattern to the database being searched, among other capabilities.

Hypercube orientations with only two indegrees 
With Joe Buhler, Steve Butler, and Ron Graham, Journal of Combinatorial Theory, Series A 118 (2011), 16951702.
We consider the problem of orienting the edges of the \(n\)dimensional hypercube so that only two
different indegrees occur. This is connected to a question arising from constructing a strategy for a "hat puzzle."

Open Problems in Euclidean Ramsey Theory 
With Ron Graham. In Ramsey Theory: Yesterday, Today and Tomorrow, A. Soifer (ed.), Birkhauser, Boston (2010), 115120.
This book chapter is a survey of open problems in Euclidean Ramsey theory, with emphasis on recent activity in the field.

Intersecting Domino Tilings 
With Steve Butler and Paul Horn. The Fibonacci Quarterly 48 (2010), 114120.
We examine a variant of the classical ErdősKoRado problem concerning maximal intersecting families of sets. In our construction,
we consider tilings of \(2 \times n\) and \(3 \times 2n\) strips by dominos, and say that any two tilings intersect if they have a domino in common.
We completely characterize the maximal intersecting families of these tilings.

Monochromatic Triangles in \(\mathbb{E}^2\) 
Geombinatorics XIX (3) (2009).
This paper is a survey of the current state of some Euclidean Ramsey problems arising from the work of Erdős,
Graham, Montgomery, Rothschild, Spencer, and Straus. It includes a few new results..
