Mathematics Research

Number Theory

Research Articles

Uniform Bounds for Digit-Appending Fibonacci Walks

The Fibonacci Quarterly, forthcoming
Simultaneous Niven Numbers in Arithmetic Progressions for Power-Related Bases

Bulletin of the Australian Mathematical Society, forthcoming
A Flanking Pattern in a Sum-of-Divisors Congruence

Working paper, 2025
Oh's 8-Universality Criterion Is Unique

Kyungpook Mathematical Journal, 2021 (preprint)
Configurations of Extremal Type II Codes via Harmonic Weight Enumerators [with N. D. Elkies]

Journal de Theorie des Nombres de Bordeaux, 2019 (preprint)
Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions [with D. M. Kane]

Canadian Mathematical Bulletin, 2014 (preprint)
Minimal S-Universality Criteria May Vary in Size [with N. D. Elkies and D. M. Kane]

Journal de Theorie des Nombres de Bordeaux, 2013 (preprint)
Weighted Generating Functions for Type II Lattices and Codes [with N. D. Elkies]

Quadratic and Higher Degree Forms, 2013 (preprint)
Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80 [with N. D. Elkies]

Proceedings of the American Mathematical Society, 2010 (preprint)
On the Classification of Type II Codes of Length 24 [with N. D. Elkies]

SIAM Journal on Discrete Mathematics, 2010 (preprint)
On Congruence Conditions for Primality [with S. Gong]

INTEGERS: The Electronic Journal of Combinatorial Number Theory, 2010
Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions [with S. Hong]

Proceedings of the American Mathematical Society, 2010 (preprint)
Configurations of Extremal Even Unimodular Lattices

International Journal of Number Theory, 2009 (preprint)
On Universal Binary Hermitian Forms

INTEGERS: The Electronic Journal of Combinatorial Number Theory, 2009 (preprint)
Uniqueness of the 2-universality Criterion

Note di Matematica, 2008
Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3) [with Z. Abel]

Journal de Theorie des Nombres de Bordeaux, 2008 (abstract; preprint)

Discrete Mathematics

Research Articles

Prisoners, Rooms, and Lightswitches [with D. M. Kane]

Electronic Journal of Combinatorics, 2021 (preprint)
A Constant Bound for the Periods of Parallel Chip-firing Games with Many Chips [with P. M. Kominers]

Archiv der Mathematik, 2010 (preprint)

Computational Geometry

Research Articles

A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in Quadratic Time [with Z. Abel, H. A. Akitaya, M. Korman, and F. Stock]

Proceedings of the International Symposium on Computational Geometry (SoCG), 2024
Hinged Dissections Exist [with T. G. Abbott, Z. Abel, D. Charlton, E. D. Demaine, and M. L. Demaine]

Discrete & Computational Geometry, 2012 (conference version, Proceedings of the 24th Annual Symposium on Computational Geometry, 2008; preprint)
Every Large Point Set contains Many Collinear Points or an Empty Pentagon [with Z. Abel, B. Ballinger, P. Bose, S. Collette, V. Dujmovic, F. Hurtado, S. Langerman, A. Por, and D. R. Wood]

Graphs and Combinatorics, 2011 (extended abstract, Proceedings of the 21st Canadian Conference on Computational Geometry; preprint)
Shape Replication Through Self-Assembly and RNase Enzymes [with Z. Abel, N. Benbernou, M. Damian, E. D. Demaine, R. Flatland, R. Schweller, and M. L. Demaine]

Proceedings of the 2010 ACM-SIAM Symposium on Discrete Algorithms, 2010

Elementary Mathematics

Research Articles

Fractal Flipbooks [with A. J. Hawksley]

Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, 2016
Flipbook Polyhedra [with A. J. Hawksley]

Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, 2013
Irrational Roots Revisited

The Mathematical Gazette, 2010
Improved Bounds on the Sizes of S.P Numbers [with P. M. Kominers]

The Mathematical Gazette, 2010
A Categorical Construction of Ultrafilters [with D. Litt and Z. Abel]

Rocky Mountain Journal of Mathematics, 2010 (preprint)

Surveys & Reviews

Finding Matrices that Satisfy Functional Equations

College Mathematics Journal, 2009 (preprint; abstract)

Public Writing

Why Today Is Math Geeks' Favorite Friday the 13th in a Century

Every, 2021
Math Geeks Must Wait 100 Years for a Day Like This

Bloomberg Opinion, 2018

Coauthors

Timothy G. Abbott (1), Zachary Abel (6), Hugo A. Akitaya (1), Brad Ballinger (1), Nadia Benbernou (1), Prosenjit Bose (1), David Charlton (1), Sebastien Collette (1), Mirela Damian (1), Erik D. Demaine (2), Martin L. Demaine (2), Vida Dujmovic (1), Noam D. Elkies (5), Robin Flatland (1), Sherry Gong (1), Andrea J. Hawksley (2), Shaofang Hong (1), Ferran Hurtado (1), Daniel M. Kane (3), Paul M. Kominers (2), Matias Korman (1), Stefan Langerman (1), Daniel Litt (1), Attila Por (1), Robert Schweller (1), Frederick Stock (1), David R. Wood (1)