Janusz Januszewski and Marek Lassak

Covering a Convex Body by Its Negative Homothetic Copies

Translative Packing of Unit Squares into Squares

Banach-Mazur Distance of Central Sections of a Centrally Symmetric Convex Body

We prove that the Banach-Mazur distance between arbitrary two central sections of co-dimension c of any centrally symmetric convex body in E is at most (2c+ 1). MSC 2000: 52A21, 46B20

On Translative Coverings of Convex Bodies

We introduce and study t-coverings in En, i.e., arrangements of proper translates of a convex body K ⊂ En sufficient to cover K. First, we investigate relations between t-coverings of the whole of K and t-coverings of its boundary only. Refining the notion of t-covering in several ways, we then derive, particularly for centrally symmetric convex bodies and n = 2, theorems which are interesting ...

On-line Algorithms for the q-adic Covering of the Unit Interval and for Covering a Cube by Cubes

We present efficient algorithms for the on-line q-adic covering of the unit interval by sequences of segments. The basic method guarantees covering provided the total length of segments is at least 1 + 2 · 1 q − 1 q3 . Other algorithms improve this estimate for q ≥ 6. The unit d-dimensional cube can be on-line covered by an arbitrary sequence of cubes whose total volume is at least 2+ 53 + 5 3 ...