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 .
Constrained and generalized barycentric Davenport constants.
Representation of finite abelian group elements by subsequence sums
Let be a finite and nontrivial abelian group with . A conjecture of Hamidoune says that if is a sequence of integers, all but at most one relatively prime to , and is a sequence over with , the maximum multiplicity of at most , and , then there exists a nontrivial subgroup such that every element can be represented as a weighted subsequence sum of the form , with a subsequence of . We give two examples showing this does not hold in general, and characterize the counterexamples...
On the Olson and the Strong Davenport constants
A subset of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of 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, -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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