منابع مشابه
Davenport constant with weights
For the cyclic group G = Z/nZ and any non-empty A ∈ Z. We define the Davenport constant of G with weight A, denoted by DA(n), to be the least natural number k such that for any sequence (x1, · · · , xk) with xi ∈ G, there exists a non-empty subsequence (xj1, · · · , xjl) and a1, · · · , al ∈ A such that ∑l i=1 aixji = 0. Similarly, we define the constant EA(n) to be the least t ∈ N such that fo...
متن کاملDavenport constant with weights and some related questions, II
Let n ∈ N and let A ⊆ Z/nZ be such that A does not contain 0 and it is non–empty. Generalizing a well known constant, EA(n) is defined to be the least t ∈ N such that for all sequences (x1, . . . , xt) ∈ Z, there exist indices j1, . . . , jn ∈ N, 1 ≤ j1 < · · · < jn ≤ t, and (θ1, · · · ,θn) ∈ A with ∑n i=1 θixji ≡ 0 (mod n). Similarly, for any such set A, we define the Davenport Constant of Z/n...
متن کاملUpper Bounds for the Davenport Constant
We prove that for all but a certain number of abelian groups of order n the Davenport constant is at most nk + k − 1 for positive integers k ≤ 7. For groups of rank three we improve on the existing bound involving the Alon-Dubiner constant.
متن کاملOn the Davenport Constant and Group Algebras
For a finite abelian group G and a splitting field K of G, let d(G, K) denote the largest integer l ∈ N for which there is a sequence S = g1 · . . . · gl over G such that (X g1 − a1) · . . . · (Xl − al) 6= 0 ∈ K[G] for all a1, . . . , al ∈ K . If D(G) denotes the Davenport constant of G, then there is the straightforward inequality D(G)−1 ≤ d(G, K). Equality holds for a variety of groups, and a...
متن کاملRemarks on a generalization of the Davenport constant
A generalization of the Davenport constant is investigated. For a finite abelian group G and a positive integer k, let D k (G) denote the smallest ℓ such that each sequence over G of length at least ℓ has k disjoint non-empty zero-sum subsequences. For general G, expanding on known results, upper and lower bounds on these invariants are investigated and it is proved that the sequence (D k (G)) ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2010
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2009.09.005