William Erickson, Ph.D.
Postdoctoral Associate
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
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(with Rebecca Bourn and Jeb F. Willenbring) Graphical methods and rings of invariants on the symmetric algebra. Canad. J. Math. To appear. arXiv:2205.08708
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The break buddy problem. Math. Mag. To appear.
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(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
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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
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(with Jan Kretschmann) The sum of width-one tensors. Enumer. Comb. Appl. 4(2023), #S2R7. https://doi.org/10.54550/ECA2024V4S1R7
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(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
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(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
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Haste makes waste: an optimization problem. College Math. J. 53(2022), 122–133. https://doi.org/10.1080/07468342.2021.2022955
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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
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(with Jan Kretschmann) The structure and normalized volume of Monge polytopes. arXiv:2311.07522
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(with Markus Hunziker) Stanley decompositions of rings of invariants and certain highest weight Harish-Chandra modules. arXiv:2310.04581
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(with Rebecca Bourn) A palindromic polynomial connecting the earth mover's distance to minuscule lattices of Type A. arXiv:2307.02652
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A Cayley–Menger formula for the earth mover’s simplex. arXiv:2306.12030
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(with Daniel Herden, Jonathan Meddaugh, Mark Sepanski, et al.) Young tableau reconstruction via minors. arXiv:2307.13161
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(with Markus Hunziker) Dimension identities, almost self-conjugate partitions, and BGG complexes for Hermitian symmetric pairs. arXiv:2301.09744
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Enright resolutions and Blattner’s formula in Type A. arXiv:2108.08469