Article ID Journal Published Year Pages File Type
8903615 European Journal of Combinatorics 2018 10 Pages PDF
Abstract
Odlyzko and Stanley introduced a greedy algorithm for constructing infinite sequences with no 3-term arithmetic progressions when beginning with a finite set with no 3-term arithmetic progressions. The sequences constructed from this procedure are known as Stanley sequences and appear to have two distinct growth rates which dictate whether the sequences are structured or chaotic. A large subclass of sequences of the former type is independent sequences, which have a self-similar structure. An attribute of interest for independent sequences is the character. In this paper, building on recent progress, we prove that every nonnegative integer λ∉{1,3,5,9,11,15} is attainable as the character of an independent Stanley sequence, thus resolving a conjecture of Rolnick.
Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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