Infinite Sidon sequences
نویسندگان
چکیده
منابع مشابه
Infinite Sidon sequences
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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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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In this paper we revisit the notion of sophistication for infinite sequences. Koppel defined sophistication of an object as the length of the shortest (finite) total program (p) that with some (finite or infinite) data (d) produce it and |p|+ |d| is smaller than the shortest description of the object plus a constant. However the notion of “description of infinite sequences” is not appropriately...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2014
ISSN: 0001-8708
DOI: 10.1016/j.aim.2014.01.011