  Finite density systems can be explored with Lattice QCD through the
calculation of multi-hadron correlation functions. Recently, systems with up to
12 $\pi^+$'s or $K^+$'s have been studied to determine the 3-$\pi^+$ and
3-$K^+$ interactions, and the corresponding chemical potentials have been
determined as a function of density. We derive recursion relations between
correlation functions that allow this work to be extended to systems of
arbitrary numbers of mesons and to systems containing many different types of
mesons, such as $\pi^+$'s, $K^+$'s, $\bar{D}^0$'s and $B^+$'s. These relations
allow for the study of finite-density systems in arbitrary volumes, and for the
study of high-density systems.
