Costa–Mella–Pasotti–Pellegrini conjecture on zero-sum simple orderings

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Let (G,+)(G,+) be an abelian group, and let TT be a finite subset of G∖{0}G\setminus\{0\} such that no 22-subset {x,−x}\{x,-x\} is contained in TT and

∑t∈Tt=0.\sum_{t\in T}t=0.

An ordering of the elements of TT is simple when its partial sums are all distinct and non-zero. Costa–Mella–Pasotti–Pellegrini conjecture. The set TT admits a simple ordering. This conjecture concerns zero-sum subsets in abelian groups and is motivated by the study of Heffter arrays. The source gives no resolution of the general case.

References

Primary source

A. Pasotti and J. H. Dinitz, “A survey of Heffter arrays”, arXiv:2209.13879 (2022).

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