### Abstract

Given a polyhedron P⊂ℝ we write P_{I} for the convex hull of the integral points in P. It is known that P_{I} can have at most 135-2 vertices if P is a rational polyhedron with size φ. Here we give an example showing that P_{I} can have as many as Ω(φ{symbol}^{n-1)} vertices. The construction uses the Dirichlet unit theorem.

Original language | English |
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Pages (from-to) | 135-142 |

Number of pages | 8 |

Journal | Combinatorica |

Volume | 12 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 1 1992 |

### Keywords

- AMS subject classification code (1991): 52C07, 11H06

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics

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## Cite this

Bárány, I., Howe, R., & Lovász, L. (1992). On integer points in polyhedra: A lower bound.

*Combinatorica*,*12*(2), 135-142. https://doi.org/10.1007/BF01204716