Published in Ergodic Theory and Dynamical Systems, 2026
Senior thesis proving ergodicity of the fast and slow triangle maps, later published in Ergodic Theory and Dynamical Systems.
Recommended citation: Garrity, T. and Lehmann Duke, J. (2026). "Ergodicity and algebraicity of the fast and slow triangle maps." Ergodic Theory and Dynamical Systems, 46(1), 93-127. https://doi.org/10.1017/etds.2025.10198
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Published in Forum of Mathematics, Sigma, 2025
Topological approach to zero-sum Ramsey theory, extending the Erdős-Ginzburg-Ziv theorem, with applications to Kneser hypergraphs.
Recommended citation: Frick, F., Lehmann Duke, J., McNamara, M., Park-Kaufmann, H., Raanes, S., Simon, S., Thornburgh, D., and Wellner, Z. (2025). "Topological methods in zero-sum Ramsey theory." Forum of Mathematics, Sigma, 13, e192. https://doi.org/10.1017/fms.2025.10125
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Published in The Fibonacci Quarterly, 2025
A short note on the interplay between math outreach and original research, growing out of questions about Zeckendorf-style decompositions.
Recommended citation: Cheigh, J., Dantas e Moura, G. Z., Lehmann Duke, J., Mauro, A., McDonald, Z., Mello, A., Miller, K., Miller, S. J., and Velazquez Iannuzzelli, S. (2025). "An invitation to Fibonacci digits." The Fibonacci Quarterly, 63(4), 702-710.
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Published in Discrete Mathematics & Theoretical Computer Science, 2023
A three-dimensional analogue of the Erdős distinct distance problem, bounding the minimum number of distinct angles determined by point configurations in general position.
Recommended citation: Ascoli, R., Betti, L., Lehmann Duke, J., Liu, X., Milgrim, W., Miller, S. J., Palsson, E. A., Romero Acosta, F., and Velazquez Iannuzzelli, S. (2023). "Distinct angles and angle chains in three dimensions." Discrete Mathematics & Theoretical Computer Science, 25(1), Combinatorics. https://doi.org/10.46298/dmtcs.10037
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Published in Combinatorial and Additive Number Theory (CANT) conference proceedings, 2023
Evidence toward Gaussian behavior in the random Zeckendorf game, building on the two-player game of Baird, Epstein, Flint, and Miller.
Recommended citation: Cheigh, J., Dantas e Moura, G. Z., Jeong, R., Lehmann Duke, J., Milgrim, W., Miller, S. J., and Ngamlamai, P. (2023). "Towards the Gaussianity of random Zeckendorf games." Combinatorial and Additive Number Theory (CANT) conference proceedings.
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