5 citations · 16 across the 11 of their papers we have counts for
11 papers
Congruences via Partitions with Exactly Two Part Sizes
Sittinon Jirattikansakul, Teeradej Kittipassorn, Kraiwich Kongsiri +2
We prove the congruence , where denotes the number of positive divisors of , for with $(A,B) \in…
Characterization of the Three-Dimensional Fivefold Translative Tiles
Mei Han, Kirati Sriamorn, Qi Yang +1
This paper proves the following statement: If a convex body can form a fivefold translative tiling in , it must be a parallelotope, a hexagonal prism, a rhombic dodec…
On the multiple illumination numbers of convex bodies
Kirati Sriamorn
In this paper, we introduce an -fold illumination number of a convex body in Euclidean space , which is the smallest number of directions required to…
The Three and Fourfold Translative Tiles in Three-Dimensional Space
Mei Han, Kirati Sriamorn, Qi Yang +1
This paper proves the following statement: If a convex body can form a three or fourfold translative tiling in the three-dimensional space, it must be a parallelohedron. In other w…
Twofold Translative Tiles in Three-Dimensional Space
Mei Han, Qi Yang, Kirati Sriamorn +1
This paper proves the following statement: {\it If a convex body can form a twofold translative tiling in , it must be a parallelohedron.} In other words, it must be…
Twofold Translative Tilings with Convex Bodies
Kirati Sriamorn
Let be a convex body. It is known that, in general, if is a -fold translative tile (for some positive integer ), then may not be a (onefold) translative tile. How…
On the Multiple Packing Densities of Triangles
Kirati Sriamorn
Given a convex disk and a positive integer , let and denote the -fold translative packing density and the -fold lattice packing density of , r…
Multiple Lattice Packings and Coverings of the Plane with Triangles
Kirati Sriamorn
Given a convex disk and a positive integer , let and denote the -fold lattice packing density and the -fold lattice covering density of $…
On the Lattice Packings and Coverings of the Plane with Convex Quadrilaterals
Kirati Sriamorn
It is well known that the lattice packing density and the lattice covering density of a triangle are and respectively. We also know that the lattices th…
On the Multiple Covering Densities of Triangles
Kirati Sriamorn, Akanat Wetayawanich
Given a convex disk and a positive integer , let and denote the -fold translative covering density and the -fold lattice covering…
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…