Polynomial-size vectors are enough for the unimodular triangulation of\n simplicial cones

2019/06/20 by Michael von Thaden, von Thaden, Michael
Computer Science · Mathematics · #11H06 #52B20 #52C07 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1906.09118

openalex publication_date 2019/06/20 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

In a recent paper, Bruns and von Thaden established a bound for the length of\nvectors involved in a unimodular triangulation of simplicial cones. The bound\nis exponential in the square of the logarithm of the multiplicity, and improves\nprevious bounds significantly. The authors mentioned that the next goal would\nbe a bound that is polynomial in the multiplicity but not knowing if such a\nbound exists. In this paper we will prove that such a bound, which is\npolynomial in the multiplicity \μ, indeed exists. In detail, the bound is of\nthe type \μ^f(d) with f(d) \∈ \O(d).\n

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