Positive-density sets A and B in the integers satisfy d(A+B)=d(A)+d(B) precisely when they are not both contained in a proper finite union of residue classes.
Kneser,Abschätzung der asymptotischen Dichte von Summenmengen, Math
3 Pith papers cite this work. Polarity classification is still indexing.
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2026 3verdicts
UNVERDICTED 3representative citing papers
For sufficiently large n with r = floor((n-1)/2), any Hamiltonian Berge cycle plus one additional edge in an n-vertex r-uniform hypergraph contains Berge cycles of all lengths 2 to n.
Every sum-free set A in F_5^n with |A| at least 28 times 5 to the n-3 is either in two parallel hyperplanes or isomorphic to a specific 28-element sum-free set in F_5^3 times the lower-dimensional space.
citing papers explorer
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An inverse theorem for sumsets of sets of positive density in the integers
Positive-density sets A and B in the integers satisfy d(A+B)=d(A)+d(B) precisely when they are not both contained in a proper finite union of residue classes.
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One extra edge forces Berge pancyclicity
For sufficiently large n with r = floor((n-1)/2), any Hamiltonian Berge cycle plus one additional edge in an n-vertex r-uniform hypergraph contains Berge cycles of all lengths 2 to n.
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Large sum-free sets in finite vector spaces II
Every sum-free set A in F_5^n with |A| at least 28 times 5 to the n-3 is either in two parallel hyperplanes or isomorphic to a specific 28-element sum-free set in F_5^3 times the lower-dimensional space.