A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with
exactly i> 0 interior lattice points. We will show that the same bound is true for the …

It is shown that, for any lattice polytope P⊂ ℝd the set int (P)∩ lℤd (provided that it is non-
empty) contains a point whose coefficient of asymmetry with respect to P is at most 8d·(8l+ 7) …

In this paper we show that the diameter of ad-dimensional lattice polytope in 0, k^ n 0, kn is
at most ⌊\left (k-1 2\right) d ⌋⌊ k-1 2 d⌋. This result implies that the diameter of ad …

Let $\Delta $ be an $ n $-dimensional lattice polytope. The smallest non-negative integer $ i
$ such that $ k\Delta $ contains no interior lattice points for $1\leq k\leq ni $ we call the …

The h∗-polynomial of a lattice polytope is the numerator of the generating function of the
Ehrhart polynomial. Let P be a lattice polytope with h∗-polynomial of degree d and with …

A well-known result by Lagarias and Ziegler states that there are finitely many equivalence
classes of d-dimensional lattice polytopes having volume at most K, for fixed constants d and …

If K is the underlying point-set of a simplicial complex of dimension at most d whose vertices
are lattice points, and if G (K) is the number of lattice points in K, then the lattice point …

A lattice polytope is a polytope in whose vertices are all in. The volume of a lattice polytope
P containing exactly k≥ 1 points in d in its interior is bounded above by. Any lattice polytope …

Consider a convex n-dimensional polytope P in R'with all vertices in the lattice En. In this
article, we give a formula for the number of lattice points in P, in the case where P is simple …

We determine lattice polytopes of smallest volume with a given number of interior lattice
points. We show that the Ehrhart polynomials of those with one interior lattice point have …