On the width of a planar convex set containing zero or one lattice points

The width of a convex set on the sphere

We study the relationship between some alternative definitions of the concept of the width of a convex set on the sphere. Those relations allow to characterize whether a convex set on the sphere can pass through a spherical interval by rigid motions. Finally, we give an optimal algorithm to compute the width on the sphere.

On the convex layers of a planar set

Let S be a set of n points in the Euclidean plane. The convex layers of S are the convex polygons obtained by iterating on the following procedure: compute the convex hull of S and remove its vertices from S. This process of peeling a planar point set is central in the study of robust estimators in statistics. It also provides valuable information on the morphology of a set of sites and has pro...

On the Rectilinear Convex Layers of a Planar Set

In this paper we give an optimal O(n log n) time and O(n) space algorithm to compute the rectilinear convex layers of a set S of n points on the plane. We also compute the rotation of S that minimizes the number of rectilinear convex layers in O(n log n) time and O(n) space.

a note on the zero divisor graph of a lattice

abstract. let $l$ be a lattice with the least element $0$. an element $xin l$ is a zero divisor if $xwedge y=0$ for some $yin l^*=lsetminus left{0right}$. the set of all zero divisors is denoted by $z(l)$. we associate a simple graph $gamma(l)$ to $l$ with vertex set $z(l)^*=z(l)setminus left{0right}$, the set of non-zero zero divisors of $l$ and distinct $x,yin z(l)^*$ are adjacent if and only...

Is There a Planar Convex Set with Given Width, Diameter, and Inradius?