On Two-Point Configurations in a Random Set
نویسندگان
چکیده
منابع مشابه
On Two-point Configurations in Random Set
We show that with high probability a random set of size Θ(n1−1/k) of {1, . . . , n} contains two elements a and a+ dk, where d is a positive integer. As a consequence, we prove an analogue of Sárközy-Fürstenberg’s theorem for random set.
متن کاملOn Two-point Configurations in a Random Set
We show that with high probability a random subset of {1, . . . , n} of size Θ(n) contains two elements a and a + d, 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}.
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We prove a transference type result for pseudo-random subsets of Z N that is analogous to the well-known Fürstenberg-Sárközy theorem. More precisely, let k 2 be an integer and let and be real numbers satisfying + ()/(2 k+1 3) > 1. Let ✓ Z N be a set with size at least N and linear bias at most N. Then, every A ✓ with relative density |A|/|| (log log N) 1 2 log log log log log N contains a pair ...
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ژورنال
عنوان ژورنال: Integers
سال: 2009
ISSN: 1867-0652
DOI: 10.1515/integ.2009.004