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Algebra & Combinatorics Seminar

Title: An extremal problem related to weighted Davenport constant
Speaker: Eshita Mazumdar (ISI, Bangalore)
Date: 31 January 2020
Time: 3 pm
Venue: LH-3, Mathematics Department

For a finite abelian group $G$ and $A \subset [1, \exp(G) - 1]$, the $A$-weighted 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. The original motivation for studying Davenport Constant was the problem of non-unique factorization in number fields. The precise value of this invariant for the cyclic group for certain sets $A$ is known but the general case is still unknown. Typically an extremal problem deals with the problem of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects that satisfies certain requirements. In a recent work with Prof. Niranjan Balachandran, we introduced an Extremal Problem for a finite abelian group related to Weighted Davenport Constant. In this talk I will talk about the behaviour of it for different groups, specially for cyclic group.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 13 Jun 2024