Counterexamples of the conjecture on roots of Ehrhart polynomials

2011/06/23 by Akihiro Higashitani, Higashitani, Akihiro · 1 citation
Mathematics · Agricultural and Biological Sciences · Chemistry · #Advanced Combinatorial Mathematics #Natural Compound Pharmacology Studies #Axial and Atropisomeric Chirality Synthesis

paper · pdf · doi:10.48550/arxiv.1106.4633

Abstract

An outstanding conjecture on roots of Ehrhart polynomials says that all roots α of the Ehrhart polynomial of an integral convex polytope of dimension d satisfy -d ≤ \Re(α) ≤ d-1. In this paper, we suggest some counterexamples of this conjecture.

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