Adjacent cycle-chains are $e$-positive
Combinatorics
2024-10-30 v1
Abstract
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 attaching a cycle to a graph preserves the -positivity of these pieces. From this, we prove an -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.
Keywords
Cite
@article{arxiv.2410.21762,
title = {Adjacent cycle-chains are $e$-positive},
author = {Foster Tom and Aarush Vailaya},
journal= {arXiv preprint arXiv:2410.21762},
year = {2024}
}
Comments
28 pages, 12 figures