ИСТИНА

We will discuss some combinatorial properties of generalized Ising-Potts models in the extremely natural formalization of Biggs (interaction model by Biggs). We will show that state sum of generalized Ising-Potts model satisfies the deletion-contraction property and express in terms of TutteGrothendieck invariants. Using these facts and the analogue of high temperature formula for classical Ising model we give a simple proof of Matiyasevich’s theorem about chromatic and flow polynomials. Also we will show proof of the ”inversion” of Matiyasevich’s theorem, which is hypothetically related with new solutions of the KP hierarchy. In conclusion we will discuss some unexpected links between graph discriminant, Tutte-Grothendieck invariants and state sum of generalized Ising-Potts model.