Fix α ∈ (0, 1/3). We show that, from a topological point of view, almost all sets A ⊆ N have the property that, if A 0 = A for all but o(n α ) elements, then A 0 is not a nontrivial sumset B + C. In particular, almost all A are totally irreducible. In addition, we prove that the measure analogue holds with α = 1.

Almost all sets of nonnegative integers and their small perturbations are not sumsets

Paolo Leonetti
Primo
2023-01-01

Abstract

Fix α ∈ (0, 1/3). We show that, from a topological point of view, almost all sets A ⊆ N have the property that, if A 0 = A for all but o(n α ) elements, then A 0 is not a nontrivial sumset B + C. In particular, almost all A are totally irreducible. In addition, we prove that the measure analogue holds with α = 1.
2023
2022
Leonetti, Paolo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2145971
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