  Recent results have placed the classical shuffle conjecture of Haglund et al.
in a broader context of an infinite family of conjectures about parking
functions in any rectangular lattice. The combinatorial side of the new
conjectures has been defined using a complicated generalization of the dinv
statistic which is composed of three parts and which is not obviously
non-negative. Here we simplify the definition of dinv, prove that it is always
non-negative, and give a geometric description of the statistic in the style of
the classical case. We go on to show that in the n x (n+1) lattice, parking
functions satisfy a fermionic formula that is similar to the one given in the
classical case by Haglund and Loehr.
