For some papers, there is a link to accompanying data or a relevant Mathematica package. The documentation for each package includes a survey of the package features and therefore also serves as a short summary of some main ideas of the paper.

research papers

• Boundary growth in one-dimensional cellular automata (with Charles Brummitt).   talk | arXiv
  packages: CellularAutomatonBoundaries.m, CellularAutomatonData.m

• Two binomial coefficient conjectures.   .ps | talk | arXiv

• p-regularity of the p-adic valuation of the Fibonacci sequence (with Luis Medina).   .ps | arXiv
  package: RegularSequences.m

• Growing words in the free group on two generators (with Bobbe Cooper), to appear in Illinois Journal of Mathematics.   .ps | talk | arXiv
  data: equivalence classes | package: EquivalentWords.m

• k-automatic sets of rational numbers (with Jeffrey Shallit), Language and Automata Theory and Applications (Proceedings) (2012) 490–501.   .ps | talk | arXiv

• The iterated integrals of ln(1 + xⁿ) (with Tewodros Amdeberhan, Christoph Koutschan, and Victor Moll), International Journal of Number Theory 8 (2012) 71–94.   .ps | arXiv | journal

• Avoiding 3/2-powers over the natural numbers (with Jeffrey Shallit), Discrete Mathematics 312 (2012) 1282–1288.   .ps | arXiv | journal

• Toward a language theoretic proof of the four color theorem (with Bobbe Cooper and Doron Zeilberger), Advances in Applied Mathematics 48 (2012) 414–431.   .ps | talk | arXiv | journal
  package: ParseWords.m

• The number of nonzero binomial coefficients modulo p^α, Journal of Combinatorics and Number Theory 3 (2011) 15–25.   .ps | talk | arXiv | journal
  package: BinomialCoefficients.m

• Iterated primitives of logarithmic powers (with Luis Medina and Victor Moll), International Journal of Number Theory 7 (2011) 623–634.   .ps | arXiv | journal

• Pattern avoidance in binary trees, Journal of Combinatorial Theory, Series A 117 (2010) 741–758.   .ps | talk | arXiv | journal
  unabridged version (with more details)
  package: TreePatterns.m

• Non-regularity of ⌊α + log_k n⌋, Integers: The Electronic Journal of Combinatorial Number Theory 10 (2010) 19–23.   .ps | arXiv | journal
  package: RegularSequences.m

• Counting interesting elections (with Lara Pudwell), The American Mathematical Monthly 117 (2010) 167–174.   .ps | arXiv | journal

• Regularity versus complexity in the binary representation of 3ⁿ, Complex Systems 18 (2009) 367–377.   .ps | arXiv | journal

• The number of walks on a regular Cayley tree (with Doron Zeilberger).   .ps | arXiv

• Bounds on the frequency of 1 in the Kolakoski word (with Elizabeth Kupin).   .ps | arXiv

• A natural prime-generating recurrence, Journal of Integer Sequences 11 (2008) 08.2.8.   .ps | talk | arXiv | journal
  blog post by Jeffrey Shallit   edition of The Mathematical Tourist by Ivars Peterson

• Local nested structure in rule 30, Complex Systems 16 (2006) 239–258.   .ps | journal
  data: right side evolution | package: BijectiveRules.m

survey articles

• Known families of integer solutions of x³ + y³ + z³ = n.
  data: list of solutions

• Elliptic curves and integral solutions to A⁴ + B⁴ + C⁴ = D⁴.

• Functional equations for the Riemann zeta function and Dirichlet L-functions.