Research Publications

  • Monochromatic Progressions in Random Colorings   (Submitted).

  • On permutations avoiding arithmetic progressions   (with Timothy D. LeSaulnier)

        Discrete Mathematics 311 (2011), 205-207.

  • On a Variant of Van der Waerden's Theorem  

        Integers 10 (2010), A17, 5pp. (electronic).

  • The Hales-Jewett number is exponential: game-theoretic consequences   (with József Beck and Wesley Pegden)

        Analytic Number Theory: Essays in Honour of Klaus Roth, Cambridge University Press (2009), 22-37.

  • On the discrepancy of quasi-progressions

        The Electronic Journal of Combinatorics 15 (2008), #R104, 14pp. (electronic).

  • Eleven Euclidean distances are enough

        Journal of Number Theory 128 (2008), 1655-1661.

  • A short proof of a theorem on degree sets of graphs   (with Amitabha Tripathi)

        Discrete Applied Mathematics 155 (2007), 670-671.

  • On the largest k-primitive subset of [1, n]

        Integers 6 (2006), A1, 3pp. (electronic).

  • Dreidel lasts O(n²) spins   (with Thomas Robinson)

        Advances in Applied Mathematics 36 (2006), 85-94.

  • On the least size of a graph with a given degree set   (with Amitabha Tripathi)

        Discrete Applied Mathematics 154 (2006), 2530-2536.

  • On a generalization of the coin exchange problem for three variables   (with Amitabha Tripathi)

        Journal of Integer Sequences 9 (2006), Article 06.4.6, 8pp. (electronic).

  • Closest approximations to real numbers   (with Amitabha Tripathi)

        Ars Combinatoria 77 (2005), 3-8.

  • Which two-sorted algebras of booleans and naturals have a finite basis?   (with Wan Fokkink and Jaco van de Pol)

        Algebra Universalis 52 (2004), 469-485.

  • A note on a theorem of Erdos and Gallai   (with Amitabha Tripathi)

        Discrete Mathematics 265 (2003), 417-420.

    Doctoral Dissertation

        Arithmetic Progressions : Combinatorial and Number-theoretic Perspectives, 2007.

    Research Interests

        Research Statement   (written in 2006, somewhat outdated)

        Ph.D. Qualifying Examination Syllabus

    Manuscripts

  • Monochromatic Van der Waerden Triples, 2006.

  • On the discrepancy of staircase sequences, 2006.

  • Extra set paradoxes, 2005.

  • A game based on a question of Erdos, 2005.

  • A tale of two square roots, 2005.

  • On the ultimate periodicity of mex sequences, 2004.

  • Fractions with bounded partial quotients, 2004.

  • One, two, three ... sorority, 2003.

    Master's Thesis

        Some problems in combinatorial number theory, 2002.