On the number of generalized Sidon sets
نویسندگان
چکیده
A set of nonnegative integers is called a Sidon if there no 4-tuple, i.e., (a, b, c, d) in with + b = c d and {a, b} ∩ {c, d} ∅. Cameron Erdős proposed the problem determining number sets [n]. Results Kohayakawa, Lee, Rodl Samotij, Saxton Thomason have established that between 2 (1.16+o(1))√n (6.442+o(1))√n . An α-generalized [n] at most α 4-tuples. One way to extend estimate We show (n/ log4 n)-generalized additional restrictions Θ(√n) In particular, log5 Our approach based on some variants graph container method.
منابع مشابه
Generalized Sidon sets
We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers, answering an old question of Simon Sidon. © 2010 Elsevier Inc. All rights reserved. MSC: 11B
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Fix integers b > a ≥ 1 with g := gcd(a, b). A set S ⊆ N is {a, b}-multiplicative if ax 6= by for all x, y ∈ S. For all n, we determine an {a, b}-multiplicative set with maximum cardinality in [n], and conclude that the maximum density of an {a, b}-multiplicative set is b b+g . Erdős [2, 3, 4] defined a set S ⊆ N to be multiplicative Sidon1 if ab = cd implies {a, b} = {c, d} for all a, b, c, d ∈...
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ژورنال
عنوان ژورنال: Acta Scientiarum Mathematicarum
سال: 2021
ISSN: ['0324-5462', '2064-8316', '0001-6969']
DOI: https://doi.org/10.14232/actasm-018-777-z