On Finite Sidon Sequences
نویسندگان
چکیده
منابع مشابه
Results on Sidon and B h Sequences
Results on Sidon and Bh Sequences Sangjune Lee A set A of non-negative integers is a Sidon set if all the sums a1 + a2, with a1 ≤ a2 and a1, a2 ∈ A, are distinct. In this dissertation, we deal with results on the number of Sidon sets in [n] = {0, 1, · · · , n − 1} and the maximum size of Sidon sets in sparse random subsets of [n] or N (the set of natural numbers). We also consider a natural gen...
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A sequence (ai) of integers is weak Sidon or well-spread if the sums ai + aj , for i < j , are all different. Let f (N) denote the maximum integer n for which there exists a weak Sidon sequence 0 a1< · · ·<an N . Using an idea of Lindström [An inequality for B2-sequences, J. Combin. Theory 6 (1969) 211–212], we offer an alternate proof that f (N)<N1/2 + O(N1/4), an inequality due to Ruzsa [Solv...
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We give the first explicit construction of an infinite Sidon sequence A with A(x) x for some c > 1/3. Our method allows to take c = √ 2− 1. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive. Our method generalizes to Bh sequences when h ≥ 3. In these case our constructions are not explicit but they give the first improvements on the...
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A subset A of the set [n] = f1; 2; : : : ; ng, jAj = k, is said to form a Sidon (or Bh) sequence, h 2, if each of the sums a1 + a2 + : : : + ah; a1 a2 : : : ah; ai 2 A, are distinct. We investigate threshold phenomena for the Sidon property, showing that if An is a random subset of [n], then the probability that An is a Bh sequence tends to unity as n ! 1 if kn = jAnj n1=2h, and that P(An is Si...
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We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solvability of some equations and the distribution of their solutions. We obtain classic and more recent results avoiding the use of exponential sums, the usual tool to deal with these problems.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1993
ISSN: 0022-314X
DOI: 10.1006/jnth.1993.1037