I have an association with classical Statistical Mechanics. You may check Asano contraction. (I am not a true St.Mech.; you may ask here our @Robert Israel, possibly others too).
This is only an association due to the form of the required polynomials. The key words are ferromagnetic models, (generalize!) Ising models, David Ruelle's monographies (the old classic "Rigorous Statistical Mechanics", and a much newer one), Joseph Slawny's papers, etc. (@Robert made significant contributions to Statistical Mechanics, and he should tell us more--my own active contact with this wonderful branch of mathematics was unfortunately short).