The zero-sum constant, the Davenport constant and their analogues
نویسندگان
چکیده
منابع مشابه
On the Davenport constant and on the structure of extremal zero-sum free sequences
Let G = Cn1 ⊕ . . .⊕Cnr with 1 < n1 | . . . |nr be a finite abelian group, d∗(G) = n1 + . . .+ nr−r, and let d(G) denote the maximal length of a zero-sum free sequence over G. Then d(G) ≥ d∗(G), and the standing conjecture is that equality holds for G = Cr n. We show that equality does not hold for C2 ⊕ Cr 2n, where n ≥ 3 is odd and r ≥ 4. This gives new information on the structure of extremal...
متن کاملDavenport 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 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 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 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: Technical Transactions
سال: 2020
ISSN: 2353-737X,0011-4561
DOI: 10.37705/techtrans/e2020027