For a finite abelian group $G$ with $\exp(G)=n$, the arithmetical invariant $\mathsf s_A(G)$ is defined to be the least integer $k$ such that any sequence $S$ with length $k$ of elements in $G$ has a $A$ weighted zero-sum subsequence of length $n$. When $A=\{1\}$, it is the Erdős-Ginzburg-Ziv constant and is denoted by $\mathsf s (G)$. For certain class of sets $A$, we already have some general bounds for these weighted constants corresponding to the cyclic group $\mathbb{Z}_n$, which was given by Griffiths. For odd integer $n$, Adhikari and Mazumdar generalized the above mentioned results in the sense that they hold for more sets $A$. In the present paper we modify Griffiths' method for even $n$ and obtain general bound for the weighted constants for certain class of weighted sets which include sets that were not covered by Griffiths for $n\equiv 0 \pmod{4}$.
@article{10_37236_6285,
author = {Eshita Mazumdar and Sneh Bala Sinha},
title = {Modification of {Griffiths'} result for even integers},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {4},
doi = {10.37236/6285},
zbl = {1431.11040},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6285/}
}
TY - JOUR
AU - Eshita Mazumdar
AU - Sneh Bala Sinha
TI - Modification of Griffiths' result for even integers
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/6285/
DO - 10.37236/6285
ID - 10_37236_6285
ER -
%0 Journal Article
%A Eshita Mazumdar
%A Sneh Bala Sinha
%T Modification of Griffiths' result for even integers
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/6285/
%R 10.37236/6285
%F 10_37236_6285
Eshita Mazumdar; Sneh Bala Sinha. Modification of Griffiths' result for even integers. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/6285
