Alladi Ramakrishnan Hall

Some combinatorial invariants for a finite abelian group

Eshita Mazumdar

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For a fnite abelian group $G$, the Davenport Constant $D_A(G)$ is defined to
be the least positive integer $k$ such that any sequence $S$ with length $k$ over $G$ has a non-empty $A$ weighted zero-sum subsequence. Similarly, the invariant
$s_A(G)$ is defined to be the least positive integer $k$ such that any sequence $S$
with length $k$ over $G$ has a non-empty $A$ weighted zero-sum subsequence of
length $exp(G)$. The precise value of these invariants for the cyclic group for
certain set $A$ is known but the general case is still an open question. In this
talk, I will present the results which we found towards this direction and also
discuss an extremal problem related to these combinatorial invariant. This is
a joint work with Prof. Niranjan Balachandran.