The maximal-length minimal zero-sum sequence conjecture
The maximal-length minimal zero-sum sequence conjecture
Let be a finite abelian group, and call a sequence over a minimal zero-sum sequence if its sum is zero and no nonempty proper subsum is zero. Write for the Davenport constant, the maximal length of a minimal zero-sum sequence over . The maximal-length minimal zero-sum sequence conjecture. If is neither cyclic nor an elementary -group, then for every minimal zero-sum sequence with , there exist and minimal zero-sum sequences , whose terms belong to , such that
A positive answer gives a structural description of sets of lengths with maximal elasticity in transfer Krull monoids over finite abelian groups. The supplied text does not state whether this conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Aqsa Bashir, Alfred Geroldinger and Qinghai Zhong, “On a zero-sum problem arising from factorization theory”, arXiv:2007.10094 (2020).
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