Introduction to the combinatorial atlas

Abstract

We give elementary self-contained proofs of the strong Mason conjecture recently proved by Anari et al. (2018) and Brändén and Huh (2020), and of the classical Alexandrov–Fenchel inequality. Both proofs use the combinatorial atlas technology recently introduced by the authors Chan and Pak (2021). We also give a formal relationship between combinatorial atlases and Lorentzian polynomials.