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Maximum number of sum-free colorings in finite abelian groups
[article]
2017
arXiv
pre-print
An r-coloring of a subset A of a finite abelian group G is called sum-free if it does not induce a monochromatic Schur triple, i.e., a triple of elements a,b,c∈ A with a+b=c. We investigate κ_r,G, the maximum number of sum-free r-colorings admitted by subsets of G, and our results show a close relationship between κ_r,G and largest sum-free sets of G. Given a sufficiently large abelian group G of type I, i.e., |G| has a prime divisor q with q≡ 2 3. For r=2,3 we show that a subset A⊂ G achieves
arXiv:1710.08352v1
fatcat:3grtl6mvabeebd4yqdgbpmuhr4