5 citations · 19 across the 12 of their papers we have counts for
12 papers
Borsuk's Problem in Metric Spaces
Jun Wang, Fei Xue, Chuanming Zong
In 1933, K. Borsuk proposed the following problem: Can every bounded set in be divided into subsets of smaller diameters? In 1965, V. G. Boltyanski and I. T. G…
Borsuk's partition problem in four-dimensional space
Jun Wang, Fei Xue
In 1933, Borsuk made a conjecture that every -dimensional bounded set can be divided into subsets of smaller diameter. Up to now, the problem is still open for $4\leq n\le…
Lower Bounds on Lattice Covering Densities of Simplices
Miao Fu, Fei Xue, Chuanming Zong
This paper presents new lower bounds for the lattice covering densities of simplices by studying the Degree-Diameter Problem for abelian Cayley digraphs. In particular, it proves t…
A note on the maximal perimeter and maximal width of a convex small polygon
Fei Xue, Yanlu Lian, Jun Wang +1
The polygon is small if its diameter equals one. When , it is still an open problem to find the maximum perimeter or the maximum width of a small -gon. Motivated by B…
On Hadwiger's covering functional for the simplex and the cross-polytope
Fei Xue, Yanlu Lian, Yuqin Zhang
In 1957, Hadwiger made a conjecture that every -dimensional convex body can be covered by translations of its interior. The Hadwiger's covering functional is the…
Packing minima and lattice points in convex bodies
Martin Henk, Matthias Schymura, Fei Xue
Motivated by long-standing conjectures on the discretization of classical inequalities in the Geometry of Numbers, we investigate a new set of parameters, which we call \emph{packi…
On the lattice point covering problem in dimension 2
Fei Xue
In this paper we study the lattice point covering property of some regular polygons in dimension 2.
On successive minima-type inequalities for the polar of a convex body
Martin Henk, Fei Xue
Motivated by conjectures of Mahler and Makai Jr., we study bounds on the volume of a convex body in terms of the successive minima of its polar body.
On the Banach-Mazur Distance between the Cube and the Crosspolytope
Fei Xue
In this note we study the Banach-Mazur distance between the -dimensional cube and the crosspolytope. Previous work shows that the distance has order , and here we will…
On the Covering Densities of Quarter-Convex Disks
Kirati Sriamorn, Fei Xue
It is conjectured that for every convex disks K, the translative covering density of K and the lattice covering density of K are identical. It is well known that this conjecture is…
A note on lattice coverings
Fei Xue, Chuanming Zong
This note presents an interesting counterexample to a basic covering problem.
Minkowski Bisectors, Minkowski Cells, and Lattice Coverings
Chuanming Zong
This article introduces and studies Minkowski Bisectors, Minkowski Cells, and Lattice Coverings.