3 papers
math.CO2026
The Tutte symmetric matrix of a graph
Foster Tom, Aarush Vailaya
We provide a matrix-based formula for the Tutte symmetric function of a graph. In particular, for any graph with a designated head and tail vertex, we describe an infinite matr…
math.CO2024
Adjacent cycle-chains are -positive
Foster Tom, Aarush Vailaya
We describe a way to decompose the chromatic symmetric function as a positive sum of smaller pieces. We show that these pieces are -positive for cycles. Then we prove that attac…
math.CO2024
Chromatic symmetric functions and change of basis
Bruce E. Sagan, Foster Tom
We prove necessary conditions for certain elementary symmetric functions, , to appear with nonzero coefficient in Stanley's chromatic symmetric function as well as in the gene…