On $q$-Counting of Noncrossing Chains and Parking Functions

Yen-Jen Cheng, Sen-Peng Eu, Tung-Shan Fu +1

For a finite Coxeter group $W$, Josuat-Vergès derived a $q$-polynomial counting the maximal chains in the lattice of noncrossing partitions of $W$ by weighting some of the covering…