An inverse theorem for additive bases
| Autor: | Dongchun Han, Yongke Qu |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Sequence Algebra and Number Theory Regular sequence Computer Science::Information Retrieval 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Elementary abelian group 0102 computer and information sciences 01 natural sciences Prime (order theory) Combinatorics TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Subgroup Integer 010201 computation theory & mathematics ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Computer Science::General Literature Order (group theory) 0101 mathematics Abelian group ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | International Journal of Number Theory. 12:1509-1518 |
| ISSN: | 1793-7310 1793-0421 |
| DOI: | 10.1142/s1793042116500937 |
| Popis: | Let [Formula: see text] be a finite abelian group of order [Formula: see text], and [Formula: see text] be the smallest prime dividing [Formula: see text]. Let [Formula: see text] be a sequence over [Formula: see text]. We say that [Formula: see text] is regular if for every proper subgroup [Formula: see text], [Formula: see text] contains at most [Formula: see text] terms from [Formula: see text]. Let [Formula: see text] be the smallest integer [Formula: see text] such that every regular sequence [Formula: see text] over [Formula: see text] of length [Formula: see text] forms an additive basis of [Formula: see text], i.e. [Formula: see text]. Recently, [Formula: see text] was determined for many abelian groups. In this paper, we determined [Formula: see text] for more abelian groups and characterize the structure of the regular sequence [Formula: see text] over [Formula: see text] of length [Formula: see text] and [Formula: see text]. |
| Databáze: | OpenAIRE |
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