Title:Power sum expansions for the Kromatic symmetric function
| Speaker | Laura Pierson |
| Affiliation | University of Waterloo |
| Location | MC 5479 |
Abstract:The Kromatic symmetric function was introduced by Crew, Pechenik, and Spirkl (2023) as a K-analogue of Stanley's chromatic symmetric function. While the chromatic symmetric function encodes proper colorings of a graph (where each vertex gets a color and adjacent vertices get different colors), the Kromatic symmetric function encodes proper set colorings (where each vertex gets a nonempty set of colors and adjacent vertices get non-overlapping color sets). The expansion of the chromatic symmetric function in the basis of power sum symmetric functions has several nice interpretations, including one in terms of source components of acyclic orientations, due to Bernardi and Nadeau (2020). We lift that expansion formula to give expansion formulas for the Kromatic symmetric function using a few different K-analogues of the power sum basis. Our expansions are based on Lyndon heaps, introduced by Lalonde (1995), which are representatives for certain equivalence classes of acyclic orientations on clan graphs (graphs formed from the original graph by removing vertices and adding extra copies of vertices).
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm,