Michael Tang
(mst0 at uw dot edu)
I am a third-year graduate student in the University of Washington's math department, studying algebraic combinatorics. My advisor is Ricky Liu.
I was an undergraduate at MIT, class of 2021, obtaining a bachelor's degree in mathematics with a minor in computer science. I lived at Next House.
I participate in the MIT Mystery Hunt, as well as many other puzzlehunts, on team NES. I also helped develop Noq, a website housing a suite of solvers for many genres of Nikoli-style logic puzzles.
Publications
- (October, 2023) Shuffle bases and quasisymmetric power sums (with Ricky Liu). available at https://arxiv.org/abs/2310.09371.
We characterize isomorphisms between the algebra QSym of quasisymmetric functions and the shuffle algebra Sh of compositions. To do so, we establish a universal property for Sh analogous to the one for QSym described by Aguiar, Bergeron, and Sottile. We then use these results to derive characterizations of quasisymmetric power sums and study some particular examples from the literature.