Upper and Lower Bounds for Chromatic Symmetric Functions

Abstract:

Tatsuyuki Hikita recently proved the Stanley–Stembridge conjecture using probabilistic methods, showing that the chromatic symmetric functions of unit interval graphs are positive in the basis of elementary symmetric functions. Finding a combinatorial interpretation for these e-coefficients remains a major open problem. Towards this goal, I will introduce sets of strong and powerful P-tableaux and conjecture that these sets undercount and overcount the e-coefficients of the chromatic symmetric function. I will then present special cases for which strong and powerful P-tableaux count certain e-coefficients exactly. 

Note: There is no pre-seminar.

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Meeting ID: 915 4733 5974