bibkey: bajnokbersonjust2022perfectrestricted
authors: B. Bajnok, C. Berson and H. A. Just
year: 2022
title: On Perfect Bases in Finite Abelian Groups
doi: 10.2140/involve.2022.15.525
url: https://arxiv.org/abs/2211.13675v1
claim: Question 6 asks whether any noncyclic group has a perfect restricted s-basis of size s + 1; the settlement proves that every such finite abelian group is cyclic.
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  - D5/S3/FiniteGroups/BajnokBersonJustPerfectRestrictedBasis
license: citation-only
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On Perfect Bases in Finite Abelian Groups

B. Bajnok, C. Berson and H. A. Just, “On Perfect Bases in Finite Abelian Groups,” Involve 15 (2022), 525–536. DOI: 10.2140/involve.2022.15.525. The arXiv version is arXiv:2211.13675v1, 24 November 2022.

The paper defines: “A is a perfect restricted s-basis of G if each element of G can be written uniquely as the sum of at most s distinct elements of A.” Question 6 asks: “Are there any noncyclic groups that have a perfect restricted s-basis of size s + 1?” The formal settlement proves the answer is no for finite abelian groups. Its decisive mechanism is the fixed-point-free toggle involution on each coset of the subgroup generated by a basis element, together with the odd order forced by the proper-subset count.

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DOI: https://doi.org/10.2140/involve.2022.15.525

Source: https://arxiv.org/abs/2211.13675v1