Generalizations of some zero sum theorems

Chintamani, Mohan N.; Moriya, B. K.

doi:10.1007/s12044-012-0058-7

Cited by 10 publications

(40 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The case when n is a prime was already considered by Adhikari and Rath in [7]. Chintamani and Moriya [8] extended some results of Adhikari, David and Urroz for non square-free integer n.…”

Section: Introductionmentioning

confidence: 78%

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

Sarkar¹

2022

Preprint

View full text Add to dashboard Cite

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 such that any sequence over G of length ℓ has a non-empty A-weighted zero-sum subsequence. Similarly, the combinatorial invariant EA(G) is defined to be the least positive integer ℓ such that any sequence over G of length ℓ has an A-weighted zero-sum subsequence of length |G|. In this article, we determine the exact value of DA(Zn), for some particular values of n, where A is the set of all cubes in Z * n . We also determine the structure of the related extremal sequence in this case.

show abstract

“…The case when n is a prime was already considered by Adhikari and Rath in [7]. Chintamani and Moriya [8] extended some results of Adhikari, David and Urroz for non square-free integer n.…”

Section: Introductionmentioning

confidence: 78%

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

Sarkar¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The next result is Corollary 1 in [5]. It is a direct consequence of Lemma 1 of [2]. 2 , where n = p r and p ≥ 7 is a prime.…”

Section: Introductionmentioning

confidence: 84%

“…It is a direct consequence of Lemma 1 of [2]. 2 , where n = p r and p ≥ 7 is a prime. Let S be a sequence in Z n such that at least three terms of S are in U (n).…”

Section: Introductionmentioning

confidence: 86%

See 1 more Smart Citation

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

Mondal¹,

Paul²,

Shameek³

2022

Preprint

View full text Add to dashboard Cite

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 sequence of k elements in G has a subsequence of consecutive terms such that some A-linear combination of its terms is zero (the identity element). We consider the group Zn and take A to be the kernel of the map given by the Jacobi symbol. For a prime divisor p of n, we also consider the setx ∈ Zn | x is a unit and x n = x p as a weight set.

show abstract

“…In this article, the following are among some of the results which we have obtained: 2 and U (p) 3 , where p is a prime, we characterize the A-extremal sequences in Z p .…”

Section: Introductionmentioning

confidence: 99%