William Erickson, Ph.D.

Education

Ph.D., University of Wisconsin-Milwaukee, 2022 (Advisor: Jeb Willenbring)

B.A., University of Notre Dame, 2010

Biography

Dr. Erickson joined the Baylor faculty in 2022.  He taught high-school and middle-school mathematics and Latin for eight years, before pursuing his doctorate at UW-Milwaukee (2016-2022).  He spent 17 happy summers teaching swim lessons and serving as head lifeguard and then manager at his hometown pool in Waukesha, Wisconsin.  He also enjoys trying out board games (occasionally designing new ones with his brothers), and playing piano for anyone who will listen.

Academic Interests and Research

Dr. Erickson's research focuses on the representation theory of Lie groups, particularly from a combinatorial perspective, along with invariant theory and algebraic statistics.

Publications

1. The Demazure product extended to biwords. Enumer. Comb. Appl. 5(2025), #S2R11.
2. (with Rebecca Bourn) Palindromicity of the numerator of a statistical generating function.  Discrete Math.  To appear.  arXiv:2307.02652
3. Expected value and a Cayley-Menger type formula for the generalized earth mover’s distance.  Algebr. Stat.  To appear.  arXiv:2406.07972
4. Generalized BGG resolutions and Blattner’s formula in Type A.  J. Lie Theory.  34(2024), 693–709.
5. (with Daniel Herden, Jonathan Meddaugh, Mark Sepanski, et al.) Young tableau reconstruction via minors. J. Combin. Theory Ser. A.  209(2025), 105950. https://doi.org/10.1016/j.jcta.2024.105950
6. The break buddy problem.  Math. Mag. 97(2004), 194–199. https://doi.org/10.1080/0025570X.2024.2312800
7. (with Rebecca Bourn and Jeb F. Willenbring) Graphical methods and rings of invariants on the symmetric algebra.  Canad. J. Math.  (2023), 1–26. http://dx.doi.org/10.4153/S0008414X23000780
8. (with Jan Kretschmann) The sum of all width-one matrices.  European J. Combin. 115(2024), 103799.  https://doi.org/10.1016/j.ejc.2023.103799
9. Comparing weighted difference and the earth mover’s distance via Young diagrams.  Discrete Math.  347(2024), 113667.  https://doi.org/10.1016/j.disc.2023.113667
10. (with Jan Kretschmann) The sum of width-one tensors.  Enumer. Comb. Appl.  4(2023), #S2R7.  https://doi.org/10.54550/ECA2024V4S1R7
11. (with Daniel Herden, Jonathan Meddaugh, Mark Sepanski, et al.)  Klein cordial trees and odd cyclic cordial friendship graphs.  Discrete Math.  346(2023), 113488.  https://doi.org/10.1016/j.disc.2023.113488
12. (with Mark Colarusso and Jeb F. Willenbring) Contingency tables and the generalized Littlewood–Richardson coefficients.  Proc. Amer. Math. Soc. 150(2022), 79–94.  https://doi.org/10.1090/proc/15731
13. Haste makes waste: an optimization problem.  College Math. J. 53(2022), 122–133. https://doi.org/10.1080/07468342.2021.2022955
14. A generalization for the expected value of the earth mover’s distance.  Algebr. Stat. 12(2021), 139–166.  DOI: 10.2140/astat.2021.12.139

Preprints

1. (with Markus Hunziker, Jonathan Meddaugh, Mark Sepanski, et al.) Robinson–Schensted shapes arising from cycle decompositions.  arXiv:2412.18058
2. (with Daniel Herden, Jonathan Meddaugh, Mark Sepanski, et al.) Limits and periodicity of metamour 2-distance graphs.  arXiv:2409.02306
3. (with Markus Hunziker) A combinatorial interpretation of the Bernstein degree of modules of covariants.   arXiv:2405.18766
4. (with Markus Hunziker) Tensor invariants for classical groups revisited.   arXiv:2401.17496
5. (with Markus Hunziker) Stanley decompositions of modules of covariants.   arXiv:2312.16749
6. (with Jan Kretschmann) The structure and normalized volume of Monge polytopes.  arXiv:2311.07522
7. (with Markus Hunziker) Dimension identities, almost self-conjugate partitions, and BGG complexes for Hermitian symmetric pairs.  arXiv:2301.09744