On e-positivity of the chromatic symmetric function

Abstract:

We prove a new signed elementary symmetric function expansion of the chromatic symmetric function. We then use sign-reversing involutions to prove \$e\$-positivity for graphs formed by joining cycles or cliques at single vertices. By considering connected partitions, we prove non-\$e\$-positivity for all trees that have either a vertex of degree at least five, or a vertex of degree four that is not adjacent to a leaf. We also prove that spiders with four legs are not \$e\$-positive.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

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Meeting ID: 915 4733 5974