منابع مشابه
A proof of the Cameron-Ku conjecture
A family of permutations A ⊂ Sn is said to be intersecting if any two permutations in A agree at some point, i.e. for any σ, π ∈ A, there is some i such that σ(i) = π(i). Deza and Frankl [3] showed that for such a family, |A| ≤ (n− 1)!. Cameron and Ku [2] showed that if equality holds then A = {σ ∈ Sn : σ(i) = j} for some i and j. They conjectured a ‘stability’ version of this result, namely th...
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A subset A of the integers is said to be sum-free if there do not exist elements x, y, z ∈ A with x+y = z. It is shown that the number of sum-free subsets of {1, . . . , N} is O(2N/2), confirming a well-known conjecture of Cameron and Erdős.
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In this paper we study sum-free subsets of the set {1, . . . , n}, that is, subsets of the first n positive integers which contain no solution to the equation x+ y = z. Cameron and Erdős conjectured in 1990 that the number of such sets is O(2). This conjecture was confirmed by Green and, independently, by Sapozhenko. Here we prove a refined version of their theorem, by showing that the number o...
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This paper takes a significant step towards confirming a long-standing and far-reaching conjecture of Peter J. Cameron and Cheryl E. Praeger. They conjectured in 1993 that there are no nontrivial block-transitive 6-designs. We prove that the Cameron-Praeger conjecture is true for the important case of non-trivial Steiner 6-designs, i.e. for 6-(v, k, λ) designs with λ = 1, except possibly when t...
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In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2011
ISSN: 0024-6107
DOI: 10.1112/jlms/jdr035