Chow and augmented Chow polynomials as evaluations of Poincaré-extended ab-indices

Abstract: We show that Chow polynomials and augmented Chow polynomials of matroids, and more generally of finite graded posets admitting R-labellings, are obtained as evaluations of their Poincar\'e-extended ab-indices. This implies in particular explicit combinatorial gamma-positive expansions for both. We then evaluate this expansion to obtain a compact expansion for the braid arrangement.