# Gaps in dense sidon sets

@inproceedings{Cilleruelo2000GapsID, title={Gaps in dense sidon sets}, author={Javier Cilleruelo}, year={2000} }

We prove that if A ⊂ [1, N ] is a Sidon set with N1/2−L elements, then any interval I ⊂ [1, N ] of length cN contains c|A|+EI elements of A, with |EI | ≤ 52N(1+ c1/2N1/8)(1+L + N−1/8), L+ = max{0, L}. In particular, if |A| = N + O(N), and g(A) is the maximum gap in A, we deduce that g(A) ? N. Also we prove that, under this condition, the exponent 3/4 is sharp.

## 12 Citations

SIDON SETS IN N

- Mathematics
- 2008

We study finite and infinite Sidon sets in N. The additive energy of two sets is used to obtain new upper bounds for the cardinalities of finite Sidon subsets of some sets as well as to provide short…

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Suppose g is a fixed positive integer. For N ≥ 2, a set A ⊂ Z ⋂ [1, N ] is called a B2[g] set if every integer n has at most g distinct representations as n = a + b with a, b ∈ A and a ≤ b. In this…

New Upper Bounds for Finite Bh Sequences

- Mathematics
- 2001

Abstract Let F h ( N ) be the maximum number of elements that can be selected from the set {1, …, N } such that all the sums a 1 +…+ a h , a 1 ⩽…⩽ a h are different. We introduce new combinatorial…

Extremal Graphs and Additive Combinatorics

- Mathematics
- 2014

In this thesis we investigate graphs that are constructed using objects from additive number theory. Sidon sets are used to construct C₄-free graphs that show ex( q² - q - 2 , C₄) > 1/2q³ - q² -…

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- Mathematics
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Generalising results of Erdős-Freud and Lindström, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing…

On an application of higher energies to Sidon sets

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Sidon sets is a classical object of Combinatorial Number theory, which was introduced by S. Sidon in [24]. A subset S of an abelian group G is a Sidon set iff all its non–zero differences are…

An Ordered Turán Problem for Bipartite Graphs

- MathematicsElectron. J. Comb.
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An ordered version of the Turan problem for bipartite graphs is introduced and the Turan number of $F$, written $\textrm{ex}(n,F)$, is investigated and shown to be the maximum number of edges in an F-free graph with $n$ vertices.

for bipartite graphs

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Let F be a graph. A graph G is F -free if it does not contain F as a subgraph. The Tur an number of F , written ex(n;F ), is the maximum number of edges in an

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