The Minkowski sum of two subsets A and B of a finite abelian group G is defined as all pairwise sums of elements of A and B: A+B = {a+b : a ∈ A, b ∈ B}. The largest size of a (k, ?)-sum-free set in G has been of interest for many years and in the case G = Z/nZ has recently been computed by Bajnok and Matzke. Motivated by sum-free sets of the torus, Kravitz introduces the noisy Minkowski sum of two sets, which can be thought of as discrete evaluations of these continuous sumsets. That is, given a noise set C, the noisy Minkowski sum is defined as A +C B = A+ B + C. We give bounds on the maximum size of a (k,?) -sum-free subset of Z/nZ under this new sum, for C equal to an arithmetic progression with common difference relatively prime to n and for any two element set C.
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