Inverse results for weighted Harborth constants
| Autor: | Dennys Ramos, Oscar Ordaz, Luz Elimar Marchan, Wolfgang A. Schmid |
|---|---|
| Přispěvatelé: | Departamento de Matemáticas, Decanato de Ciencias y Tecnologías, Universidad Centroccidental Lisandro Alvarado, Universidad Centroccidental Lisandro Alvarado [Venezuela] (UCLA), Laboratorio MoST, Centro ISYS, Facultad de Ciencias, Universidad Central de Venezuela, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Postgrado de la Facultad de Ciencias de la U.C.V., Faculty of Science project, the Banco Central de Venezuela, ANR-12-BS01-0011,CAESAR,Combinatoire Additive: Ensembles, Séquences et Applications Remarquables(2012) |
| Rok vydání: | 2016 |
| Předmět: |
Cyclic group
0102 computer and information sciences 01 natural sciences Combinatorics [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] Subsequence FOS: Mathematics Zero-sum problem Mathematics - Combinatorics Order (group theory) Number Theory (math.NT) 0101 mathematics Abelian group Mathematics Algebra and Number Theory Mathematics - Number Theory MSC 11B30 finite abelian group weighted subsum Direct sum 010102 general mathematics Square-free integer [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 010201 computation theory & mathematics zero-sum problem Combinatorics (math.CO) Constant (mathematics) |
| Zdroj: | International Journal of Number Theory. 12:1845-1861 |
| ISSN: | 1793-7310 1793-0421 |
| Popis: | For a finite abelian group [Formula: see text], the Harborth constant is defined as the smallest integer [Formula: see text] such that each squarefree sequence over [Formula: see text] of length [Formula: see text] has a subsequence of length equal to the exponent of [Formula: see text] whose terms sum to [Formula: see text]. The plus-minus weighted Harborth constant is defined in the same way except that the existence of a plus-minus weighted subsum equaling [Formula: see text] is required, that is, when forming the sum one can choose a sign for each term. The inverse problem associated to these constants is the problem of determining the structure of squarefree sequences of maximal length that do not yet have such a zero-subsum. We solve the inverse problems associated to these constants for certain groups, in particular, for groups that are the direct sum of a cyclic group and a group of order two. Moreover, we obtain some results for the plus-minus weighted Erdős–Ginzburg–Ziv constant. |
| Databáze: | OpenAIRE |
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