Roots of Ehrhart polynomials of Gorenstein Fano polytopes

Details Roots of Ehrhart polynomials of Gorenstein Fano polytopes Roots of Ehrhart polynomials of Gorenstein Fano polytopes

2010-01-23

arxiv.org/abs/1001.4165v1

Mathematics

Combinatorics

6 pages

Scientific paper

Given arbitrary integers $k$ and $d$ with $0 \leq 2k \leq d$, we construct a Gorenstein Fano polytope $\Pc \subset \RR^d$ of dimension $d$ such that (i) its Ehrhart polynomial $i(\Pc, n)$ possesses $d$ distinct roots; (ii) $i(\Pc, n)$ possesses exactly $2k$ imaginary roots; (iii) $i(\Pc, n)$ possesses exactly $d - 2k$ real roots; (iv) the real part of each of the imaginary roots is equal to $- 1 / 2$; (v) all of the real roots belong to the open interval $(-1, 0)$.

Affiliated with

Also associated with

No associations

Rating

Roots of Ehrhart polynomials of Gorenstein Fano polytopes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Roots of Ehrhart polynomials of Gorenstein Fano polytopes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Roots of Ehrhart polynomials of Gorenstein Fano polytopes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-515158