Pré-Publication, Document De Travail Année : 2024

SETS OF CROSS NUMBERS OF SEQUENCES OVER FINITE ABELIAN GROUPS

Aqsa Bashir
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Résumé

Let G be a finite abelian group with exp(G) the exponent of G. Then W(G) denotes the set of cross numbers of minimal zero-sum sequences over G and w(G) denotes the set of all cross numbers of non-trivial zero-sum free sequences over G. It is clear that W(G) and w(G) are bounded subsets of 1exp(G)N with maximum K(G) and k(G), respectively (here K(G) and k(G) denote the large and the small cross number of G, respectively). We give results on the structure of W(G) and w(G). We first show that both sets contain long arithmetic progressions and that only close to the maximum there might be some gaps. Then, we provide groups for which W(G) and w(G) actually are arithmetic progressions, and argue that this is rather a rare phenomenon. Finally, we provide some results in case there are gaps.
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Dates et versions

hal-04546837 , version 1 (15-04-2024)
hal-04546837 , version 2 (20-01-2025)

Identifiants

  • HAL Id : hal-04546837 , version 1

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Aqsa Bashir, Wolfgang Schmid. SETS OF CROSS NUMBERS OF SEQUENCES OVER FINITE ABELIAN GROUPS. 2024. ⟨hal-04546837v1⟩
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