  Research in combinatorics has often explored the asymmetric simple exclusion
process (ASEP). The ASEP, inspired by examples from statistical mechanics,
involves particles of various species moving around a lattice. With the
traditional ASEP particles of a given species can move but do not change
species. In this paper a new combinatorial formalism, the DASEP (doubly
asymmetric simple exclusion process), is explored. The DASEP is inspired by
biological processes where, unlike the ASEP, the particles can change from one
species to another. The combinatorics of the DASEP on a one dimensional lattice
are explored, including the associated generating function. The stationary
probabilities of the DASEP are explored, and results are proven relating these
stationary probabilities to those of the simpler ASEP.
