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Representation of finite abelian group elements by subsequence sums

David J. Grynkiewicz; Luz E. Marchan; Oscar Ordaz — 2009

Journal de Théorie des Nombres de Bordeaux

Let $G ≅ C_{n_{1}} \oplus ... \oplus C_{n_{r}}$ be a finite and nontrivial abelian group with $n_{1} | n_{2} | ... | n_{r}$ . A conjecture of Hamidoune says that if $W = w_{1} \cdot ... \cdot w_{n}$ is a sequence of integers, all but at most one relatively prime to $| G |$ , and $S$ is a sequence over $G$ with $| S | \geq | W | + | G | - 1 \geq | G | + 1$ , the maximum multiplicity of $S$ at most $| W |$ , and $σ (W) \equiv 0 mod | G |$ , then there exists a nontrivial subgroup $H$ such that every element $g \in H$ can be represented as a weighted subsequence sum of the form $g = \underset{i = 1}{\sum^{n}} w_{i} s_{i}$ , with $s_{1} \cdot ... \cdot s_{n}$ a subsequence of $S$ . We give two examples showing this does not hold in general, and characterize the counterexamples...

On the Olson and the Strong Davenport constants

Oscar Ordaz; Andreas Philipp; Irene Santos; Wolfgang A. Schmid — 2011

Journal de Théorie des Nombres de Bordeaux

A subset $S$ of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of $S$ is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, $p$ -groups with large rank relative to the exponent, including all groups with exponent at most five. These results are derived as consequences of more general...

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Currently displaying 1 – 10 of 10

Representation of finite abelian group elements by subsequence sums

On the Olson and the Strong Davenport constants

The Erdős-Ginzburg-Ziv theorem in Abelian non-cyclic groups.

Barycentric-sum problems: a survey.

On zero free sets.

Barycentric Ramsey numbers for small graphs.

Hamiltonian cycles and Hamiltonian-biconnectedness in bipartite digraphs.

Hamiltonian virus-free digraphs.

Maximum line-free set geometry in $ℤ_{3}^{d}$ .

Constrained and generalized barycentric Davenport constants.