2024/10/29 by Foster Tom, Tom, Foster, Aarush Vailaya +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · #Gene Regulatory Network Analysis
paper · pdf · doi:10.48550/arxiv.2410.21762
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 attaching a cycle to a graph preserves the e-positivity of these pieces. From this, we prove an e-positive formula for graphs of cycles connected at adjacent vertices. We extend these results to graphs formed by connecting a sequence of cycles and cliques.