We consider shifts of a set A⊆N by elements from another set B⊆N, and prove intersection properties according to the relative asymptotic size of A and B. A consequence of our main theorem is the following: If A={a_n} is such that a_n=o(n^(k/k−1)), then the k-recurrence set R_k(A)={x∣|A∩(A+x)|≥k} contains the distance sets of arbitrarily large finite sets.
Intersections of shifted sets
DI NASSO, MAURO
2015-01-01
Abstract
We consider shifts of a set A⊆N by elements from another set B⊆N, and prove intersection properties according to the relative asymptotic size of A and B. A consequence of our main theorem is the following: If A={a_n} is such that a_n=o(n^(k/k−1)), then the k-recurrence set R_k(A)={x∣|A∩(A+x)|≥k} contains the distance sets of arbitrarily large finite sets.File in questo prodotto:
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