2020/01/02 by Rachel Zhang, Zhang, Rachel
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2001.00327
openalex publication_date 2020/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, ℓ)-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, ℓ)-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.