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@YCor I just wanted to emphasize that, in additive combinatorics, zero-sum sequences (over Abelian groups) are always defined, AFAIK, as unordered sequences
@YCor A zero-sum sequence over an Abelian group G is commonly defined as an element of the free Abelian monoid over G such that etc. So, there is really no difference here between the nr of zero-sum sequences of length k over G and the nr of multisubsets of G with k elements (counted with repetition) that add up to 0.
