J ul 2 00 9 Preprint , arXiv : 0810 . 0467 LINEAR EXTENSION OF THE ERDŐS - HEILBRONN CONJECTURE
نویسنده
چکیده
The famous Erd˝ os-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erd˝ os-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements a where p(F) is the additive order of the multiplicative identity of F , and δ ∈ {0, 1} takes the value 1 if and only if n = 2 and a 1 + a 2 = 0. In this paper we prove the conjecture of Sun when p(F) n(3n − 5)/2. We also obtain a nontrivial lower bound for the cardinality of the restricted sumset
منابع مشابه
1 9 A ug 2 00 9 Preprint , arXiv : 0810 . 0467 LINEAR EXTENSION OF THE ERDŐS - HEILBRONN CONJECTURE
The famous Erd˝ os-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erd˝ os-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements a where p(F) is the additive order of the multiplicative identity of F , and δ ∈ {0, 1} takes the value ...
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The famous Erdős-Heilbronn conjecture plays an important role in the development of additive combinatorial number theory. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erdős-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements a1, . . . , an of F , we have |{a1x1 + · · ·+ anxn : x1, . . . , xn ∈ A, and xi 6= xj if i 6= ...
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In 1964 P. Erdős and H. Heilbronn [EH] made the following challenging conjecture: If p is a prime, then for any subset A of the finite field Z/pZ we have |{x1 + x2 : x1, x2 ∈ A and x1 6= x2}| > min{p, 2|A| − 3}. It had remained open for thirty years until it was confirmed fully by Dias da Silva and Hamidoune [DH] who actually obtained the following generalization with help of the representation...
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تاریخ انتشار 2009