  Thermodynamics in the strong coupling limit of lattice QCD has features which
may be similar to those of continuum QCD, such as a chiral critical end point
and a nuclear liquid gas transition. Here I compare the combinatorics of
staggered and Wilson fermions in the strong coupling limit for arbitrary number
of colors and flavors. The partition functions can be considered as an
expansions in hadronic spatial hoppings from the static limit, where both
discretizations can be expressed via formulae with coefficients of distinct
combinatorial interpretation. The corresponding multiplicites of hadronic
states are evaluated using generalizations of Catalan numbers and Lucas
polynomials. I outline how quantum Monte Carlo simulations can be carried out
in general, and summarize recent results on the gauge corrections to the strong
coupling limit.
