• Corpus ID: 238407767

# 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}
}```
• Published 6 October 2021
• Mathematics
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 .
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
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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Generalization of some weighted zero-sum theorems
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• Mathematics
Proceedings - Mathematical Sciences
• 2021
Let G be a finite abelian group of exponent n and let A be a non-empty subset of \$\$[1,n-1]\$\$ [ 1 , n - 1 ] . The Davenport constant of G with weight A , denoted by \$\$D_A(G)\$\$ D A ( G ) , is defined
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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