# On a different weighted zero-sum constant

@inproceedings{Mondal2021OnAD, title={On a different weighted zero-sum constant}, author={Santanu Mondal and Krishnendu Paul and Shameek Paul}, year={2021} }

For a ﬁnite abelian group ( G, +), the constant C ( G ) is deﬁned to be the smallest natural number k , such that any sequence of k elements in G has a subsequence of consecutive terms whose sum is zero. We also deﬁne a weighted version of this constant and determine its value for some particular weights, for the group Z n .

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## 6 Citations

Extremal sequences for a weighted zero-sum constant

- Mathematics
- 2021

For an abelian group G, the constant C(G) is defined to be the smallest natural number k, such that any sequence of k elements in G has a subsequence of consecutive terms whose sum is zero (the…

Extremal sequences for a particular weighted zero-sum constant

- Mathematics
- 2021

For an abelian group G, the constant C(G) is defined to be the smallest natural number k, such that any sequence of k elements in G has a subsequence of consecutive terms whose sum is zero (the…

On a weighted zero-sum constant related to the Jacobi symbol

- Mathematics
- 2022

For a finite abelian group (G,+) of exponent m ≥ 2 and for a nonempty set A ⊆ {1, 2, . . . ,m−1}, the A-weighted zero-sum constant CA(G) is defined to be the smallest natural number k, such that any…

Two square weighted zero-sum constants

- Mathematics
- 2022

The constant DA(n) is defined to be the smallest natural number k, such that any sequence of k elements in Zn has a subsequence whose Aweighted sum is zero. i.e. some linear combination of its terms…

Generalization of some weighted zero-sum theorems and related Extremal sequence

- Mathematics
- 2022

Let G be a finite abelian group of exponent n and let A be a non-empty subset of [1, n − 1]. The Davenport constant of G with weight A, denoted by DA(G), is defined to be the least positive integer l…

M ar 2 02 2 On unit weighted zero-sum constants of Z n

- Mathematics
- 2022

The A-weighted Gao constant EA(n) is defined to be the smallest natural number k, such that any sequence of k elements in Zn has a subsequence of length n, whose A-weighted sum is zero. When A = U(n)…

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where p is a prime and r ≥ 2. As | B | = p r−1 (p−1), so, if p ≡ 2 (mod 3), then the homomorphism from B → B given by x → x 3 has trivial kernel. Hence

- Remark: Let B = U (p r )

Let A = U (n) 3 , where n = p r and p is a prime such that p = 3, 7. Let S be a sequence in Z n such that at least four elements of S are in U (n). Then, S is an A-weighted zero-sum sequence