AbstractWe study the problem of discrepancy of finite point sets in the unit square with respect to convex polygons, when the directions of the edges are fixed, when the number of edges is bounded, as well as when no such restrictions are imposed. In all three cases, we obtain estimates for the supremum norm that are very close to best possible
In the present paper, we study the geometric discrepancy with respect to families of rotated rectang...
Gardner et al. posed the problem to find a discrete analogue of Meyer’s inequality bounding from bel...
AbstractWe consider a generalization of Heilbronn’s triangle problem by asking, given any integers n...
We study the problem of discrepancy of finite point sets in the unit square with respect to convex p...
AbstractWe study the problem of discrepancy of finite point sets in the unit square with respect to ...
We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set c...
For a finite point set $P \subset \mathbb{R}^d$, denote by $\text{diam}(P)$ the ratio of the largest...
AbstractThe irregularities of distribution of lattice points on spheres and on level surfaces of pol...
AbstractLetP⊂[0,1]dbe ann-point set and letw:P→[0,∞) be a weight function withw(P)=∑z∈Pw(z)=1. TheL2...
AbstractThe L2-discrepancy measures the irregularity of the distribution of a finite point set. In t...
AbstractLet a set of points in the Euclidean plane be given. We are going to investigate the levels ...
AbstractLet nk denote the number of times the kth largest distance occurs among a set S of n points....
AbstractWe study the problem of partitioning point sets in the space so that each equivalence class ...
For A, a finite set of points in Rd , let ∆(A) denote the spread of A and be equal to the ratio of t...
We prove that roughly points chosen uniformly and independently from a centered convex body K in yie...
In the present paper, we study the geometric discrepancy with respect to families of rotated rectang...
Gardner et al. posed the problem to find a discrete analogue of Meyer’s inequality bounding from bel...
AbstractWe consider a generalization of Heilbronn’s triangle problem by asking, given any integers n...
We study the problem of discrepancy of finite point sets in the unit square with respect to convex p...
AbstractWe study the problem of discrepancy of finite point sets in the unit square with respect to ...
We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set c...
For a finite point set $P \subset \mathbb{R}^d$, denote by $\text{diam}(P)$ the ratio of the largest...
AbstractThe irregularities of distribution of lattice points on spheres and on level surfaces of pol...
AbstractLetP⊂[0,1]dbe ann-point set and letw:P→[0,∞) be a weight function withw(P)=∑z∈Pw(z)=1. TheL2...
AbstractThe L2-discrepancy measures the irregularity of the distribution of a finite point set. In t...
AbstractLet a set of points in the Euclidean plane be given. We are going to investigate the levels ...
AbstractLet nk denote the number of times the kth largest distance occurs among a set S of n points....
AbstractWe study the problem of partitioning point sets in the space so that each equivalence class ...
For A, a finite set of points in Rd , let ∆(A) denote the spread of A and be equal to the ratio of t...
We prove that roughly points chosen uniformly and independently from a centered convex body K in yie...
In the present paper, we study the geometric discrepancy with respect to families of rotated rectang...
Gardner et al. posed the problem to find a discrete analogue of Meyer’s inequality bounding from bel...
AbstractWe consider a generalization of Heilbronn’s triangle problem by asking, given any integers n...
DOI
Add to ORKG