منابع مشابه
Progress on Poset-free Families of Subsets
Increasing attention is being paid to the study of families of subsets of an nset that contain no subposet P . Especially, we are interested in such families of maximum size given P and n. For certain P this problem is solved for general n, while for other P it is extremely challenging to find even an approximate solution for large n. It is conjectured that for any P , the maximum size is asymp...
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In this paper, we present some generalizations of Gowers’s result about product-free subsets of groups. For any group G of order n, a subset A of G is said to be product-free if there is no solution of the equation ab = c with a, b, c ∈ A. Previous results showed that the size of any product-free subset of G is at most n/δ1/3, where δ is the smallest dimension of a nontrivial representation of ...
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Let F {A(1): < i < t, t 2}, be a finite collection of finite, palrwlse disjoint subsets of Z+. Let SC R\{0} and A Z+ be finite sets. Denote by S A {i=isi:a A, i S, the s i are not ncesarily dlstinct }. For S and F as above we say that S is F-free if for every A(i), A(J) F, i J, SA(1)(% SA(j) . We prove that for S and F as above, S contains an F-free subset Q such that This result generalizes ea...
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Let G be a finite additively written abelian group, and let X be a subset of 7 elements in G. We show that if X contains no nonempty subset with sum zero, then the number of the elements which can be expressed as the sum over a nonempty subsequence of X is at least 24.
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2. R. H. Brück, Analogues of the ring of rational integers, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 50-57. 3. I. M. H. Etherington, Non-associative arithmetics, Proceedings of the Royal Society of Edinburgh vol. 62 (1949) pp. 442-453. 4. Trevor Evans, On multiplicative systems defined by generators and relations, I. Normal form theorems, Proc. Cambridge Philos. Soc. vol. 47 (1951) pp. 637-649....
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1935
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-25-1-200-208