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An Infinite Sidon Sequence

✍ Scribed by Imre Z Ruzsa


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
261 KB
Volume
68
Category
Article
ISSN
0022-314X

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✦ Synopsis


We show the existence of an infinite Sidon sequence such that the number of elements in [1, N] is N -2&1+o(1) for all large N.


πŸ“œ SIMILAR VOLUMES


Random Sidon Sequences
✍ Anant P. Godbole; Svante Janson; Nicholas W. Locantore Jr.; Rebecca Rapoport πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 154 KB

A subset A of the set [n]=[1, 2, ..., n], |A| =k, is said to form a Sidon (or B h ) sequence, h 2, if each of the sums a 1 +a 2 + } } } +a h , a 1 a 2 } } } a h ; a i # A, are distinct. We investigate threshold phenomena for the Sidon property, showing that if A n is a random subset of [n], then the

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A set \(A\) of integers is called a \(B_{h}\)-sequence if all sums \(a_{1}+\cdots+a_{h}\), where \(a_{i} \in A\), are distinct up to rearrangement of the summands. Let \(F_{h}(n)\) (resp. \(\left.f_{h}(n)\right)\) denote the size of a largest \(B_{h}\)-sequence (resp. \(B_{h}\)-sequence for \(\mathb

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In this paper we are interested in graphs which, in a sense, are a generalization of strongly regular graphs. We remind the reader that a strongly regular graph with parameters n, k, A, p (notation SRG(n, k, A, p)) is a graph on it vertices, regular of degree k, and such that any two vertices joined