COEFFICIENTS AND ROOTS OF EHRHART POLYNOMIALS
By M. Beck, J. D. Loera, M. Develin, Julian Pfeifle, R. Stanley. 2004
107 citations recorded by the source corpus.
The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coeffi- cients of Ehrhart polynomials and relate them to known inequalities. We also investigate the roots of Ehrhart polynomials. We prove that for fixed d, there exists a bounded region of C containing all roots of Ehrhart polynomials of d-polytopes, and that all real roots of these polynomials lie in (−d, ⌊d/2⌋). In contrast, we prove that when the dimension d is not fixed the positive real roots can be arbitrarily large. We finish with an experimental investigation of the Ehrhart polynomials of cyclic polytopes and 0/1-polytopes.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/42a0eb32d12fd62e3aeaa35f592aa021cc23d792
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
In Mathematical Physics
Citations in the corpus
- Roots of Ehrhart polynomials arising from graphs (2010, unknown): “Since an edge polytope is a kind of 0/1-polytope, the points in Figure 1 for V 9 are similar to those in Figure 6 of [3].”
- Ehrhart polynomials and successive minima (2005, background): “For relations among the coefficients of the Ehrhart polynomial we refer to [11, 5].”