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On Two-Point Configurations in a Random Set
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Hoi H. Nguyen
Published/Copyright:
May 7, 2009
Abstract
We show that with high probability a random subset of {1, . . . , n} of size Θ(n1–1/k) contains two elements a and a + dk, where d is a positive integer. As a consequence, we prove an analogue of the Sárközy–Fürstenberg theorem for a random subset of {1, . . . , n}.
Received: 2008-08-02
Accepted: 2009-01-03
Published Online: 2009-05-07
Published in Print: 2009-April
© de Gruyter 2009
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Articles in the same Issue
- On k-Imperfect Numbers
- On Universal Binary Hermitian Forms
- The Shortest Game of Chinese Checkers and Related Problems
- On Two-Point Configurations in a Random Set
- On Rapid Generation of SL2(𝔽q)
- Tiling Proofs of Some Formulas for the Pell Numbers of Odd Index
- Some new van der Waerden numbers and some van der Waerden-type numbers
- Integer Partitions into Arithmetic Progressions with an Odd Common Difference
- On Asymptotic Constants Related to Products of Bernoulli Numbers and Factorials
