Vertex-Maximal Lattice Polytopes Contained in 2-Simplices

Jan-Philipp Litza; Christoph Pegel; Kirsten Schmitz

Vertex-Maximal Lattice Polytopes Contained in 2-Simplices

Combinatorics 2018-05-28 v1

Authors: Jan-Philipp Litza , Christoph Pegel , Kirsten Schmitz

Abstract

Motivated by the problem of bounding the number of rays of plane tropical curves we study the following question: Given $n\in\mathbb{N}$ and a unimodular $2$ -simplex $\Delta$ what is the maximal number of vertices a lattice polytope contained in $n\cdot \Delta$ can have? We determine this number for an infinite subset of $\mathbb{N}$ by providing a family of vertex-maximal polytopes and give bounds for the other cases.

Keywords

polytopes

Cite

@article{arxiv.1805.09989,
  title  = {Vertex-Maximal Lattice Polytopes Contained in 2-Simplices},
  author = {Jan-Philipp Litza and Christoph Pegel and Kirsten Schmitz},
  journal= {arXiv preprint arXiv:1805.09989},
  year   = {2018}
}

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13 pages, 7 figures

Vertex-Maximal Lattice Polytopes Contained in 2-Simplices

Abstract

Keywords

Cite

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