  The notion of parking sequences is a new generalization of parking functions
introduced by Ehrenborg and Happ. In the parking process defining the classical
parking functions, instead of each car only taking one parking space, we allow
the cars to have different sizes and each takes up a number of adjacent parking
spaces after a trailer $T$ parked on the first $z-1$ spots. A preference
sequence in which all the cars are able to park is called a parking sequence.
In this paper, we study increasing parking sequences and count them via
bijections to lattice paths with right boundaries. Then we study two notions of
invariance in parking sequences and present various characterizations and
enumerative results.
