English

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

R2 v1 2026-06-24T10:00:18.097Z