Abstract
For an n-dimensional lattice simplex with vertices given by the standard basis vectors and
where
has positive entries, we investigate when the Ehrhart
-polynomial for
factors as a product of geometric series in powers of z. Our motivation is a theorem of Rodriguez-Villegas implying that when the
-polynomial of a lattice polytope P has all roots on the unit circle, then the Ehrhart polynomial of P has positive coefficients. We focus on those
for which
has only two or three distinct entries, providing both theoretical results and conjectures/questions motivated by experimental evidence.
2010 Mathematics Subject Classification:
Disclosure statement
No potential conflict of interest was reported by the authors.