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Hadwiger's conjecture holds for strongly monotypic polytopes

Vuong Bui

Abstract

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

Hadwiger's conjecture holds for strongly monotypic polytopes

Abstract

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.
Paper Structure (3 sections, 6 theorems, 10 equations)

This paper contains 3 sections, 6 theorems, 10 equations.

Table of Contents

  1. Introduction
  2. The proof for strongly monotypic polytopes
  3. Some discussions on monotypic polytopes

Key Result

Theorem 1

A polytope $P$ is monotypic if and only if every two disjoint primitive subsets $V_1,V_2$ of the set of normals $N(P)$ satisfies $\mathop{\mathrm{pos}}\nolimits V_1\cap \mathop{\mathrm{pos}}\nolimits V_2=\{0\}$.

Theorems & Definitions (11)

  • Conjecture 1: Hadwiger's conjecture hadwiger1972ungeloste
  • Conjecture 2: Boltyanski's illumination conjecture boltyanski1960problem
  • Theorem 1: McMullen--Schneider--Shephard 1974 mcmullen1974monotypic
  • Proposition 1
  • proof
  • Theorem 2: Bui 2023 bui2023every
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • ...and 1 more