Combinatorics of Lattice QCD at Strong Coupling

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.