2 citations · 3 across the 10 of their papers we have counts for
10 papers
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…
On Landau-Kato inequalities via semigroup orbits
Yi C. Huang, Yanlu Lian, Fei Xue
Let . Given a strongly continuous semigroup on a Banach space and an element satisfying the exponential orbital estimates $$\|e^{tA}f\|\leq…
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…
On lattice tilings of by limited magnitude error balls
Tao Zhang, Yanlu Lian, Gennian Ge
Limited magnitude error model has applications in flash memory. In this model, a perfect code is equivalent to a tiling of by limited magnitude error balls. In this…
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…
Divide bounded sets into sets having smaller diameters
Yanlu Lian, Senlin Wu
For each positive integer and each real finite dimensional Banach space , we set to be the infimum of such that each set having diameter $…
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…