Eric Tressler

I am a mathematician and computer scientist working for the IRS. I graduated from the University of California, San Diego in 2010, working under Ronald Graham; from 2010 to 2014 I worked as a researcher at HRL Laboratories, LLC.

You can find my CV here, and you can reach me at tressler@gmail.com.

Research problems
Minimizing monochromatic arithmetic progressions in \([1,n]\)	If we 2-color the integers from 1 to \(n\), how few monochromatic arithmetic progressions can we have? This question was explored in this paper of Butler, Costello, and Graham. Trying to answer this question with computer calculations gives a surprising pattern.

Tools
\(\LaTeX\) sandbox	A simple text box that interacts with MathJax to allow \(\LaTeX\) expressions to be quickly tested.

Publications
The First Nontrivial Hales-Jewett Number is Four	With Neil Hindman. Ars Combinatoria 113 (2014), 385-390. We prove that the Hales-Jewett number \(HJ(3,2)\) is 4; that is, if the length 4 words over the alphabet \(\{1,2,3\}\) are 2-colored, 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 in-degrees	With Joe Buhler, Steve Butler, and Ron Graham, Journal of Combinatorial Theory, Series A 118 (2011), 1695-1702. We consider the problem of orienting the edges of the \(n\)-dimensional hypercube so that only two different in-degrees 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), 115-120. 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), 114-120. We examine a variant of the classical Erdős-Ko-Rado 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..