A parking function (c₁, ... , c_n) can be viewed as having n cars trying to park on a one-way street with n parking spots from left to right, where car i tries to park in spot c_i, and otherwise it parks in the leftmost available spot after c_i. Another way to view this is that each car has a set C_i of "acceptable" parking spots, namely C_i = [c_i, n], and that each car tries to park in the leftmost available spot that it finds acceptable.

Motivated by this, we define a subset parking function (C₁, ... , C_n), with each C_i a subset of {1, ... , n}, by having the ith car try to park in the leftmost available element of C_i. We further generalize this idea by restricting our sets to be of size k, intervals, and intervals of length k. In each of these cases we provide formulas for the number of such parking functions.