Translated geometric progressions and covering systems
نویسندگان
چکیده
منابع مشابه
On Partial Covering For Geometric Set Systems
We study a generalization of the Set Cover problem called the Partial Set Cover in the context of geometric set systems. The input to this problem is a set system (X ,S), where X is a set of elements and S is a collection of subsets of X , and an integer k ≤ |X |. The goal is to cover at least k elements of X by using a minimum-weight collection of sets from S. In the geometric version, X typic...
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Several papers have investigated sequences which have no k-term arithmetic progressions, finding bounds on their density and looking at sequences generated by greedy algorithms. Rankin in 1960 suggested looking at sequences without k-term geometric progressions, and constructed such sequences for each k with positive density. In this paper we improve on Rankin’s results, derive upper bounds, an...
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In this work, we present a single unified framework that can solve many geometric covering queries such as inspection and mold-design. The suggested framework reduces a geometric covering query to the classic computer science set-covering problem. The solution is of exponential complexity due to the inherent complexity of the classic set-covering problem. However, in practice, we are able to ef...
متن کاملGeometric Progressions on Elliptic Curves.
In this paper, we look at long geometric progressions on different model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huff curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinate (or y-coordinate) are in geometric progression. We find infinite families of t...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1978
ISSN: 0528-2195
DOI: 10.21136/cpm.1978.108625