#### Alladi Ramakrishnan Hall

#### Some combinatorial invariants for a finite abelian group

#### Eshita Mazumdar

##### -

*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.

Done