Abstract:
In this work, we introduce the $\alpha$-chromatic symmetric functions, extending the chromatic symmetric functions defined by Shareshian and Wachs by introducing an additional real parameter $\alpha$.
We present positive combinatorial formulas and provide explicit interpretations. Notably, we show an explicit monomial expansion in terms of the $\alpha$-binomial basis and an expansion into certain chromatic symmetric functions in terms of the $\alpha$-falling factorial basis. Among various connections with other subjects, we highlight a significant link to $q$-rook theory, including a new solution to the $q$-hit problem posed by Garsia and Remmel in their 1986 paper introducing $q$-rook polynomials.
This is based on joint work with Jim Haglund and Jaeseong Oh.
$\alpha$-Chromatic symmetric functions
18.07.2024 10:30 - 11:30
Organiser:
AGDM
Location: