For several papers, there is a link to accompanying data or a related *Mathematica* package.

- The lexicographically least square-free word with a given prefix (with Siddharth Berera, Andrés Gómez-Colunga, Joey Lakerdas-Gayle, John López, Mauditra Matin, Daniel Roebuck, Noam Scully, and Juliet Whidden). arXiv
- Limiting density of the Fibonacci sequence modulo powers of
*p*(with Nicholas Bragman). arXiv - Lucas' theorem modulo
*p*^{2},*The American Mathematical Monthly***129**(2022) 846–855. arXiv | journal - Ultimate periodicity problem for linear numeration systems (with Émilie Charlier, Adeline Massuir, and Michel Rigo),
*International Journal of Algebra and Computation***32**(2022) 561–596. arXiv | journal - Lucas congruences for the Apéry numbers modulo
*p*^{2}(with Reem Yassawi and Christian Krattenthaler),*Integers***21**(2021) A20. arXiv | journal

talk: slides - Automaticity and invariant measures of linear cellular automata (with Reem Yassawi),
*Canadian Journal of Mathematics***72**(2020) 1691–1726. arXiv | journal - Avoiding 5/4-powers on the alphabet of nonnegative integers (with Manon Stipulanti),
*The Electronic Journal of Combinatorics***27**(2020) #P3.42. arXiv | journal

proceedings version: Avoiding 5/4-powers on the alphabet of nonnegative integers (extended abstract), Developments in Language Theory, edited by Nataša Jonoska and Dmytro Savchuk,*Lecture Notes in Computer Science***12086**(2020) 280–293. journal

computations: notebook | talk: slides - A closed-form solution might be given by a tree: valuations of quadratic polynomials (with Leyda Almodóvar, Alyssa Byrnes, Julie Fink, Xiao Guan, Aashita Kesarwani, Gary Lavigne, Luis Medina, Victor Moll, Isabelle Nogues, Senthil Rajasekaran, and Amber Yuan),
*SCIENTIA, Series A: Mathematical Sciences***29**(2019) 11–28. journal - IntegerSequences: a package for computing with
*k*-regular sequences, International Congress on Mathematical Software,*Lecture Notes in Computer Science***10931**(2018) 414–421. notebook version | journal

package: IntegerSequences | talk: slides - Avoiding fractional powers over the natural numbers (with Lara Pudwell),
*The Electronic Journal of Combinatorics***25**(2018) #P2.27. arXiv | journal

data: prefixes of*a*/*b*-power-free words | package: SymbolicWords | computations: notebook | talk: slides - A matrix generalization of a theorem of Fine,
*Integers***18A**(2018) A18. arXiv | journal

proceedings version: Binomial coefficients, valuations, and words, Developments in Language Theory,*Lecture Notes in Computer Science***10396**(2017) 68–74. journal | MR

talk: slides - Periodicity in the
*p*-adic valuation of a polynomial (with Luis Medina and Victor Moll),*Journal of Number Theory***180**(2017) 139–153. arXiv | journal | MR

talk: slides *p*-adic asymptotic properties of constant-recursive sequences (with Reem Yassawi),*Indagationes Mathematicae***28**(2017) 205–220. arXiv | journal | MR- Profinite automata (with Reem Yassawi),
*Advances in Applied Mathematics***85**(2017) 60–83. arXiv | journal | MR - Decision algorithms for Fibonacci-automatic words, II: related sequences and avoidability (with Chen Fei Du, Hamoon Mousavi, Luke Schaeffer, and Jeffrey Shallit),
*Theoretical Computer Science***657**(2017) 146–162. journal | MR - Infinite products arising in paperfolding (with Leyda Almodóvar, Victor Moll, Hadrian Quan, Fernando Roman, and Michole Washington),
*Journal of Integer Sequences***19**(2016) 16.5.1. journal | MR - What's in YOUR wallet? (with Lara Pudwell),
*The Mathematical Intelligencer***37**(2015) 54–60. arXiv | journal | MR

data: transition matrices | package: PocketChange | computations: notebook

media coverage:*Scientific American*blog post by Evelyn Lamb *p*-regularity of the*p*-adic valuation of the Fibonacci sequence (with Luis Medina),*The Fibonacci Quarterly***53**(2015) 265–271. arXiv | journal | MR- Automatic sets of rational numbers (with Jeffrey Shallit),
*International Journal of Foundations of Computer Science***26**(2015) 343–365. arXiv | journal | MR

proceedings version:*k*-automatic sets of rational numbers, 6th International Conference, Language and Automata Theory and Applications 2012, edited by Adrian-Horia Dediu and Carlos Martín-Vide,*Lecture Notes in Computer Science***7183**(2012) 490–501. journal | MR

talk: slides - Automatic congruences for diagonals of rational functions (with Reem Yassawi),
*Journal de Théorie des Nombres de Bordeaux***27**(2015) 245–288. arXiv | journal | MR

data: Motzkin numbers modulo*p*^{α}| package: IntegerSequences | computations: notebook | talk: slides - Classification of automorphic conjugacy classes in the free group on two generators (with Bobbe Cooper), Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography, edited by Delaram Kahrobaei and Vladimir Shpilrain,
*Contemporary Mathematics***633**(2015) 13–40. arXiv | journal | MR

data: automorphic conjugacy classes | package: EquivalentWords | talk: slides - What is … an automatic sequence?,
*Notices of the American Mathematical Society***62**(2015) 274–276. journal | MR

in the same issue: About the cover (and the cover) by Bill Casselman - A new approach to the 2-regularity of the
*l*-abelian complexity of 2-automatic sequences (with Aline Parreau, Michel Rigo, and Élise Vandomme),*The Electronic Journal of Combinatorics***22**(2015) #P1.27. arXiv | journal | MR

talk: slides - A characterization of
*p*-automatic sequences as columns of linear cellular automata (with Reem Yassawi),*Advances in Applied Mathematics***63**(2015) 68–89. arXiv | journal | MR

talk: slides - Structure and enumeration of (3+1)-free posets (with Mathieu Guay-Paquet and Alejandro Morales),
*Annals of Combinatorics***18**(2014) 645–674. arXiv | journal | MR

proceedings version: Structure and enumeration of (3+1)-free posets (extended abstract), 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013),*Discrete Mathematics & Theoretical Computer Science Proceedings*(2013) 253–264. arXiv | journal - A case study in meta-automation: automatic generation of congruence automata for combinatorial sequences (with Doron Zeilberger),
*Journal of Difference Equations and Applications***20**(2014) 973–988. arXiv | journal | MR

packages: AutoSquared (along with sample input and output), IntegerSequences - The rational–transcendental dichotomy of Mahler functions (with Jason Bell and Michael Coons),
*Journal of Integer Sequences***16**(2013) 13.2.10. arXiv | journal | MR - Growing words in the free group on two generators (with Bobbe Cooper),
*Illinois Journal of Mathematics***55**(2011) 417–426. arXiv | journal | MR

data: automorphic conjugacy classes | package: EquivalentWords | talk: slides - Boundary growth in one-dimensional cellular automata (with Charles Brummitt),
*Complex Systems***21**(2012) 85–116. arXiv | journal | MR

packages: CellularAutomatonBoundaries, CellularAutomatonData | talk: slides - The iterated integrals of ln(1 +
*x*^{n}) (with Tewodros Amdeberhan, Christoph Koutschan, and Victor Moll),*International Journal of Number Theory***8**(2012) 71–94. arXiv | journal | MR - Avoiding 3/2-powers over the natural numbers (with Jeffrey Shallit),
*Discrete Mathematics***312**(2012) 1282–1288. arXiv | journal | MR - Toward a language theoretic proof of the four color theorem (with Bobbe Cooper and Doron Zeilberger),
*Advances in Applied Mathematics***48**(2012) 414–431. arXiv | journal | MR

package: ParseWords | talk: slides - Two binomial coefficient conjectures. arXiv

This is the written version of a talk I gave at Doron Zeilberger's 60th birthday conference. At some point I plan to expand it.

talk: slides - The number of nonzero binomial coefficients modulo
*p*^{α},*Journal of Combinatorics and Number Theory***3**(2011) 15–25. arXiv | journal | MR

package: BinomialCoefficients | talk: slides - Iterated primitives of logarithmic powers (with Luis Medina and Victor Moll),
*International Journal of Number Theory***7**(2011) 623–634. arXiv | journal | MR - Pattern avoidance in binary trees,
*Journal of Combinatorial Theory, Series A***117**(2010) 741–758. arXiv | journal | MR

unabridged version (with more details)

package: TreePatterns | talk: slides - Non-regularity of ⌊
*α*+ log_{k}*n*⌋,*Integers***10**(2010) 19–23. arXiv | journal | MR - Counting interesting elections (with Lara Pudwell),
*The American Mathematical Monthly***117**(2010) 167–174. arXiv | journal | MR - Regularity versus complexity in the binary representation of 3
^{n},*Complex Systems***18**(2009) 367–377. arXiv | journal | MR - The number of walks on a regular Cayley tree (with Doron Zeilberger),
*The Personal Journal of Shalosh B. Ekhad and Doron Zeilberger*(2009). arXiv | journal - Bounds on the frequency of 1 in the Kolakoski word (with Elizabeth Kupin). arXiv

Although this paper has been cited in the literature, it is unpublished. After posting the initial version, Jean-Paul Allouche informed us of Chvátal's technical report in which he obtains better bounds using a different method. - A natural prime-generating recurrence,
*Journal of Integer Sequences***11**(2008) 08.2.8. arXiv | journal | MR

talk: slides

media coverage:*Pour la Science*article by Jean-Paul Delahaye blog post by Brian Hayes edition of*The Mathematical Tourist*by Ivars Peterson blog post by Jeffrey Shallit - Local nested structure in rule 30,
*Complex Systems***16**(2006) 239–258. journal | MR

data: right border evolution | package: BijectiveRules