Abstract. For a finite Coxeter group [Formula: see text], Josuat-Vergès derived a [Formula: see text]-polynomial counting the maximal chains in the lattice of noncrossing partitions of [Formula: see text] by weighting some of the covering relations, which we call bad edges, in these chains with a parameter [Formula: see text]. We study the connection of these weighted chains with parking functions of type [Formula: see text] ([Formula: see text], respectively) from the perspective of the [Formula: see text]-polynomial. The [Formula: see text]-polynomial turns out to be the generating function for parking functions (of either type) with respect to the number of cars that do not park in their preferred spaces. In either case, we present a bijective result that carries bad edges to unlucky cars while preserving their relative order. Using this, we give an interpretation of the [Formula: see text]-positivity of the [Formula: see text]-polynomial in the case when [Formula: see text] is the hyperoctahedral group.

A permutation σ ∈ $\frak{S}_n$ is simsun if for all k, the subword of σ restricted to {1, . . . , k} does not have three consecutive decreasing elements. The permutation σ is double simsun if both σ and σ−1 are simsun. In this paper, we present a new