منابع مشابه
The number of maximal sum-free subsets of integers
Cameron and Erdős [6] raised the question of how many maximal sum-free sets there are in {1, . . . , n}, giving a lower bound of 2bn/4c. In this paper we prove that there are in fact at most 2(1/4+o(1))n maximal sum-free sets in {1, . . . , n}. Our proof makes use of container and removal lemmas of Green [8, 9] as well as a result of Deshouillers, Freiman, Sós and Temkin [7] on the structure of...
متن کاملSharp bound on the number of maximal sum-free subsets of integers
Cameron and Erdős [6] asked whether the number of maximal sum-free sets in {1, . . . , n} is much smaller than the number of sum-free sets. In the same paper they gave a lower bound of 2bn/4c for the number of maximal sum-free sets. Here, we prove the following: For each 1 ≤ i ≤ 4, there is a constant Ci such that, given any n ≡ i mod 4, {1, . . . , n} contains (Ci + o(1))2 n/4 maximal sum-free...
متن کاملdetermination of maximal singularity free zones in the workspace of parallel manipulator
due to the limiting workspace of parallel manipulator and regarding to finding the trajectory planning of singularity free at workspace is difficult, so finding a best solution that can develop a technique to determine the singularity-free zones in the workspace of parallel manipulators is highly important. in this thesis a simple and new technique are presented to determine the maximal singula...
15 صفحه اولIntersection Properties of Subsets of Integers
Intersection properties of sets have been widely investigated by many authors. One type of theorems proved for them has the following form [9]. Let S be an n-element set and AI. ... , AN £ S, 1 £ [1, n]. Assume that IAi I1Ajl E 1 for 1,,;;;; i <j ,,;;;;N. How large can N be under this condition, depending on n and I? Thus, e.g., the de Bruijn-Erdos theorem [1] asserts that if IAi I1Ajl = 1 for ...
متن کاملInfinite Subsets of Random Sets of Integers
There is an infinite subset of a Martin-Löf random set of integers that does not compute any Martin-Löf random set of integers. To prove this, we show that each real of positive effective Hausdorff dimension computes an infinite subset of a Martin-Löf random set of integers, and apply a result of Miller.
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ژورنال
عنوان ژورنال: International Journal of Combinatorics
سال: 2015
ISSN: 1687-9163,1687-9171
DOI: 10.1155/2015/216475