On Lev's periodicity conjecture
Christian Reiher

TL;DR
This paper classifies large sum-free subsets in finite vector spaces over F_3, resolving Lev's periodicity conjecture by establishing bounds on maximal aperiodic sum-free sets.
Contribution
It provides a complete classification of sum-free subsets exceeding a certain density and proves Lev's conjecture on the maximal size of aperiodic sum-free sets.
Findings
Classified sum-free subsets with density > 1/6 in F_3^n
Resolved Lev's periodicity conjecture for all n
Established optimal bounds for maximal aperiodic sum-free sets
Abstract
We classify the sum-free subsets of whose density exceeds . This yields a resolution of Vsevolod Lev's periodicity conjecture, which asserts that if a sum-free subset is maximal with respect to inclusion and aperiodic (in the sense that there is no non-zero vector satisfying ), then -- a bound known to be optimal if , while for there are no such sets.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Graph theory and applications · Mathematics and Applications
