Foster Tom

activity

20242026

collaborators

5 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 $G$ with a designated head and tail vertex, we describe an infinite matr…

math.CO2026

Linear relations on star coefficients of the chromatic symmetric function

Rosa Orellana, Foster Tom

We prove that the coefficient of the star $st_{2 1^{n - 2}}$ in the chromatic symmetric function $X_{G}$ determines whether a connected graph $G$ is $2$ -connected. We also pr…

math.CO2026

Graphs missing a connected partition

Foster Tom

We prove that a graph with a cut vertex whose deletion produces at least five connected components must be missing a connected partition of some type. We prove that this also holds…

math.CO2025

The chromatic symmetric function of graphs glued at a single vertex

Foster Tom, Aarush Vailaya

We describe how the chromatic symmetric function of two graphs glued at a single vertex can be expressed as a matrix multiplication using certain information of the two individual…

math.CO2024

Adjacent cycle-chains are $e$ -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 $e$ -positive for cycles. Then we prove that attac…

The Tutte symmetric matrix of a graph

Linear relations on star coefficients of the chromatic symmetric function

Graphs missing a connected partition

The chromatic symmetric function of graphs glued at a single vertex

Adjacent cycle-chains are e-positive

Adjacent cycle-chains are $e$ -positive