With several nice collaborators, we finished the first stage of a project that came out of last summer’s AMS MRC on Algebraic Combinatorics. Building off of our group leader Rosa Orellana‘s experience in the area, we studied the chromatic symmetric function of unicyclic graphs. We found several nice formulas including some that generalize recent work of her and her students on trees, as well as some interesting phenomena pertaining only to graphs with cycles. Like most good projects, we came out with a lot more questions than those we were able to answer, and some of us will likely continue working in this area.
One of the fun things about this project was learning about various graph algorithms and methods of computing the CSF. I will post some of the Jupyter notebooks with code we found helpful under the Code area soon. Also keep an eye out for forthcoming work on principal specialization of CSFs with another cohort from the MRC!
I’m also excited that my article with Fernando Díaz on shellability and posets of rook placements (sects) has been accepted for publication in the Electronic Journal of Combinatorics. It should appear at some point this summer. Finally, an article on starting and running a math circle at a county jail will appear in another fine publication (Journal of Humanistic Mathematics), probably this July.