Introduction to the combinatorial atlas
Combinatorics
2022-12-23 v1 Metric Geometry
Abstract
We give elementary self-contained proofs of the strong Mason conjecture recently proved by Anari at. al. (arXiv:1811.01600) and Br\"and\'en--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.
Keywords
Cite
@article{arxiv.2203.01533,
title = {Introduction to the combinatorial atlas},
author = {Swee Hong Chan and Igor Pak},
journal= {arXiv preprint arXiv:2203.01533},
year = {2022}
}
Comments
28 pages, 2 figures. arXiv admin note: text overlap with arXiv:2110.10740