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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…
Classification and enumeration of lattice polygons in a disc
Qiuyue Liu, Yuqin Zhang, Zhanyuan Cai
In 1980, V. I. Arnold studied the classification problem for convex lattice polygons of given area. Since then, this problem and its analogues have been studied by many authors, in…
Lower Bound on Translative Covering Density of Tetrahedra
Yiming Li, Miao Fu, Yuqin Zhang
In this paper, we present the first nontrivial lower bound on the translative covering density of tetrahedra. To this end, we show the lower bound, in any translative covering of 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…
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…