2021/06/04 by White, Jacob A
#(primary) 05E05 #(secondary) 05E18 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2106.02665
We introduce a quasisymmetric class function associated with a group acting on a double poset or on a directed graph. The latter is a generalization of the chromatic quasisymmetric function of a digraph introduced by Ellzey, while the latter is a generalization of a quasisymmetric function introduced by Grinberg. We prove representation-theoretic analogues of classical and recent results, including F-positivity, and combinatorial reciprocity theorems. We also deduce results for orbital quasisymmetric functions. We also study a generalization of the notion of strongly flawless sequences.