Abelian group

Zero sum maps on finite abelian groups are given by permutations

Let be a finite abelian group of order and be a function. Then satisfies iff there exists a permutation

of such that .¹ comb

Proof

We first show that given a permutation

whose differences are , we can find another whose differences are such that , i.e. the same except in two places.

See op. cit.

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Footnotes

1. 1952. A Combinatorial Problem on Abelian Groups ↩