Introduction to the combinatorial atlas

Abstract

We give elementary self-contained proofs of the strong Mason conjecture recently proved by Anari at. al. (arXiv:1811.01600) and Brändén--Huh (arXiv:1902.03719), and of the classical Alexandrov--Fenchel inequality. Both proofs use the combinatorial atlas technology recently introduced by the authors (arXiv:2110.10740). We also give a formal relationship between combinatorial atlases and Lorentzian polynomials.

28 pages, 2 figures. arXiv admin note: text overlap with arXiv:2110.10740

References in corpus (2)

• Lorentzian polynomials on cones and the Heron-Rota-Welsh conjecture
• Log-concave poset inequalities

Cited by in corpus (4)

• Equality cases of the Alexandrov--Fenchel inequality are not in the polynomial hierarchy
• Effective poset inequalities
• On the cross-product conjecture for the number of linear extensions
• Correlation inequalities for linear extensions