The multivariate arithmetic Tutte polynomial

Source abstract

We introduce an arithmetic version of the multivariate Tutte polynomial and a quasi-polynomial that interpolates between the two. A generalized Fortuin-Kasteleyn representation with applications to arithmetic colorings and flows is obtained. We give a new and more general proof of the positivity of the coefficients of the arithmetic Tutte polynomial and (in the representable case) a geometrical interpretation of them.