Tiling, packing, and covering by clusters
This long paper represents a very nice and attractive survey in the theory of tiling, packing and covering by clusters. Recall that a cluster is a union of a finite number of cubes from the standard lattice of cubes. The author presents mainly the results of Everett, Galovich, Hamaker, Hickerson, Loomis, Newman, Stein and Szabo. The paper contains six sections: Clusters, The cross and semicross, Multiplier sets, The multiplier set \(\{\) 1,2,...,k\(\}\), The multiplier set \(\{\pm 1,\pm 2,...,\pm k\}\), Origins. Each section is divided into two or three subsections and contains many important notions and results in this field. There are also many open questions and results that suggest lines of further investigation. A rich and suggestive bibliography in this field is given.
tiling, packing and covering by clusters
scientific article; zbMATH DE number 3973731