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Discordant sets and ergodic Ramsey theory.
We explore the properties of non-piecewise syndetic sets with positive (upper) density, which we call discordant, as they arise in combinatorics, number theory, ergodic theory, and topological and symbolic dynamics.
Joint work Rushil Raghavan supervised by Vitaly Bergelson.
The chromatic B-symmetric function and acyclic orientations of signed graphs.
The chromatic B-symmetric function is a generalization of Stanley's chromatic symmetric function to signed graphs.
We study this function as it relates to acyclic orientations of signed graphs and obtain a joint generalization of theorems of Stanley and Zaslavsky.
Joint work with Eric Fawcett, Torey Hilbert, Kat Husar, Hannah Johnson, and Mikey Riley supervised by Sergei Chmutov. In preparation.
The chromatic symmetric function and Stanley's tree conjecture.
Stanley's tree conjecture asks whether the chromatic symmetric function distinguishes non-isomorphic trees.
A partial positive result is obtained, showing that a special class of trees (generalizing the notion of a spider) is distinguished.
Supervised by Sergei Chmutov.
Published in Involve 13.1 (2020), pp. 109–116.
material from talks