Interval parking functions

Interval parking functions (IPFs) are a generalization of ordinary in which each car is willing to park only fixed interval spaces. Each function can be expressed as pair (a,b), where and b dual function. We say that permutations (x,y) reachable if there an IPF (a,b) such x,y the outcomes a,b, respectively, functions. Reachability reflexive antisymmetric, but not general transitive. prove its transitive closure, pseudoreachability order, precisely bubble-sorting order on symmetric group Sn, terms normal form permutation sense du Cloux; particular, it isomorphic product chains lengths 2,…,n. It thus seen special case Armstrong's sorting lies between Bruhat (left) weak orders.