4 papers
Proper circular arc graphs are -positive
Aarush Vailaya
We prove an -positive formula for the chromatic symmetric function of proper circular arc graphs solving the case of a conjecture of Ellzey and of Alexandersson and Panova…
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…
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…
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…