Rogers, C. A.; Zong, C. Covering convex bodies by translates of convex bodies. (English) Zbl 0884.52018 Mathematika 44, No. 1, 215-218 (1997). Hadwiger conjectured that the smallest number of translates of a convex body \(K\) required to cover \(K\) is \(2^n\). Here a number of known weaker estimates of the number of required translates, or lattice translates, are obtained as consequences of two simple results. Reviewer: E.Heil (Darmstadt) Cited in 1 ReviewCited in 20 Documents MSC: 52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry) 52A30 Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.) 52A40 Inequalities and extremum problems involving convexity in convex geometry Keywords:covering; lattice covering; illumination PDFBibTeX XMLCite \textit{C. A. Rogers} and \textit{C. Zong}, Mathematika 44, No. 1, 215--218 (1997; Zbl 0884.52018) Full Text: DOI References: [1] Chakerian, Canad. J. Math. 17 pp 497– (1965) · Zbl 0137.15302 [2] DOI: 10.1017/CBO9780511569258 [3] Bezdek, Beitrdge Algebra Geom. 35 pp 131– (1994) [4] Bezdek, New Trends in Discrete and Computational Geometry pp 199– (1994) [5] DOI: 10.1007/BF01876622 · Zbl 0826.52018 [6] Grünbaum, Proc. Svmpos. Pure Math. 1 pp 233– (1963) [7] DOI: 10.1007/BF01899997 · Zbl 0082.15703 [8] Rogers, Mathematika 6 pp 33– (1959) [9] Rogers, Mathematika 4 pp 1– (1957) [10] Hadwiger, Elem. Math. 12 pp 121– (1957) [11] Rogers, Packing and Covering (1964) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.