2 citations · 3 across the 10 of their papers we have counts for
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The lattice covering density of the regular octahedron
Yanlu Lian, Fei Xue
We prove that the lattice covering density of the regular octahedron is , settling a conjecture of Dougherty and Faber.
Non-Separable Homothetic Triangles, Part I: Constructions and Lower Bounds
Yanlu Lian, Fei Xue, Qihui Yuan
A finite family of planar convex bodies is called a non-separable family if no line disjoint from its union has at least one member in each open half-plane. In this paper, we prove…
Minimal Covering Bodies and a Minkowski-Type Criterion for Lattice Coverings
Yanlu Lian, Fei Xue
We study convex bodies whose translates by a fixed lattice cover space and for which every proper convex subbody loses this property. In three dimensions, the convex hull of indepe…
Lower Bound on Translative Covering Density of Octahedron
Yiming Li, Yanlu Lian, Miao Fu +1
In this paper, we present the first nontrivial lower bound on the translative covering density of octahedron. To this end, we show the lower bound, in any translative covering of o…
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…
Covering the crosspolytope with its smaller homothetic copies
Yanlu Lian, Yuqin zhang
In 1957, Hadwiger made the famous conjecture that any convex body of -dimensional Euclidean space can be covered by smaller positive homothetic copies. Up t…