S D Adhikari
Articles written in Proceedings – Mathematical Sciences
Volume 118 Issue 2 May 2008 pp 183-188 Research Articles
Some Zero-Sum Constants with Weights
S D Adhikari R Balasubramanian F Pappalardi P Rath
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.
Volume 119 Issue 3 June 2009 pp 275-281
Remarks on some Zero-Sum Theorems
S D Adhikari Sanoli Gun Purusottam Rath
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.
Volume 120 Issue 3 June 2010 pp 259-266
Zero-Sum Problems with Subgroup Weights
S D Adhikari A A Ambily B Sury
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.
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