منابع مشابه
On Various Restricted Sumsets
For finite subsets A1, . . . , An of a field, their sumset is given by {a1+ · · ·+an : a1 ∈ A1, . . . , an ∈ An}. In this paper we study various restricted sumsets of A1, . . . , An with restrictions of the following forms: ai − aj 6∈ Sij , or αiai 6= αjaj , or ai + bi 6≡ aj + bj (mod mij). Furthermore, we gain an insight into relations among recent results on this area obtained in quite differ...
متن کاملOn Snevily's conjecture and restricted sumsets
Let G be an additive abelian group whose finite subgroups are all cyclic. Let A1, . . . , An (n > 1) be finite subsets of G with cardinality k > 0, and let b1, . . . , bn be pairwise distinct elements of G with odd order. We show that for every positive integer m 6 (k−1)/(n−1) there are more than (k− 1)n− (m+1) (n 2 ) sets {a1, . . . , an} such that a1 ∈ A1, . . . , an ∈ An, and both ai 6= aj a...
متن کاملRestricted Sumsets and a Conjecture of Lev
Let A, B, S be finite subsets of an abelian group G. Suppose that the restricted sumset C = {a + b: a ∈ A, b ∈ B, and a − b 6∈ S} is nonempty and some c ∈ C can be written as a + b with a ∈ A and b ∈ B in at most m ways. We show that if G is torsion-free or elementary abelian then |C| > |A| + |B| − |S| − m. We also prove that |C| > |A| + |B| − 2|S| − m if the torsion subgroup of G is cyclic. In...
متن کاملAn Additive Theorem and Restricted Sumsets
Abstract. Let G be any additive abelian group with cyclic torsion subgroup, and let A, B and C be finite subsets of G with cardinality n > 0. We show that there is a numbering {ai} n i=1 of the elements of A, a numbering {bi} n i=1 of the elements of B and a numbering {ci} n i=1 of the elements of C, such that all the sums ai + bi + ci (1 6 i 6 n) are distinct. Consequently, each sub-cube of th...
متن کاملOn two questions about restricted sumsets in finite abelian groups
Let G be an abelian group of finite order n, and let h be a positive integer. A subset A of G is called weakly h-incomplete if not every element of G can be written as the sum of h distinct elements of A; in particular, if A does not contain h distinct elements that add to zero, then A is called weakly h-zero-sum-free. We investigate the maximum size of weakly hincomplete and weakly h-zero-sum-...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2005
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2005.06.004