Articles written in Proceedings – Mathematical Sciences

• Some Zero-Sum Constants with Weights

For an abelian group 𝐺, the Davenport constant $D(G)$ is defined to be the smallest natural number 𝑘 such that any sequence of 𝑘 elements in 𝐺 has a non-empty subsequence whose sum is zero (the identity element). Motivated by some recent developments around the notion of Davenport constant with weights, we study them in some basic cases. We also define a new combinatorial invariant related to $(\mathbb{Z}/n\mathbb{Z})^d$, more in the spirit of some constants considered by Harborth and others and obtain its exact value in the case of $(\mathbb{Z}/n\mathbb{Z})^2$ where 𝑛 is an odd integer.

• Remarks on some Zero-Sum Theorems

In the present paper, we give a new proof of a weighted generalization of a result of Gao in a particular case. We also give new methods for determining the weighted Davenport constant and another similar constant for some particular weights.

• Zero-Sum Problems with Subgroup Weights

In this note, we generalize some theorems on zero-sums with weights from [1], [4] and [5] in two directions. In particular, we consider $\mathbb{Z}^d_p$ for a general 𝑑 and subgroups of $Z^∗_p$ as weights.

• Proceedings – Mathematical Sciences

Volume 131, 2021
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• Editorial Note on Continuous Article Publication

Posted on July 25, 2019