Exactly solvable irreversible processes on one-dimensional lattices

We consider the kinetics of a process where the sites of an infinite 1-D lattice are filled irreversibly and, in general, cooperatively by N-mers (taking N consecutive sites at a time). We extend the previously available exact solution for nearest neighbor cooperative effects to range N cooperative effects. Connection with the continuous ‘‘cooperative car parking problem’’ is indicated. Both uniform and periodic lattices, and empty and certain partially filled lattice initial conditions are considered. We also treat monomer ‘‘filling in stages’’ for certain highly autoinhibitory cooperative effects of arbitrary range.