On the index of length four minimal zero-sum sequences
نویسندگان
چکیده
منابع مشابه
MINIMAL ZERO-SUM SEQUENCES OF MAXIMUM LENGTH IN THE GROUP C3 ⊕ C3k
A sequence α in an additively written abelian group G is called a minimal zero-sum sequence if its sum is the zero element of G and none of its proper subsequences has sum zero. This note characterizes the minimal zero-sum sequences of maximum length in the group C3⊕C3k. Let α be a sequence in an additively written finite abelian group G; its sum and length will be denoted by σ(α) and |α|, resp...
متن کاملLong Minimal Zero - Sum Sequences in the Groups
The article discusses su ciently long minimal zero-sum sequences over groups of the form C 1 2 C2k, with rank r 3. Their structure is clarified by general results in the first part. The conclusions are applied to the Davenport problems, direct and inverse, for the rank-5 group C4 2 C2k. We determine its Davenport constant for k 70 and describe the longest minimal zero-sum sequences in the more ...
متن کاملOn Short Zero-sum Subsequences of Zero-sum Sequences
Abstract. Let G be a finite abelian group, and let η(G) be the smallest integer d such that every sequence over G of length at least d contains a zero-sum subsequence T with length |T | ∈ [1, exp(G)]. In this paper, we investigate the question whether all non-cyclic finite abelian groups G share with the following property: There exists at least one integer t ∈ [exp(G)+1, η(G)− 1] such that eve...
متن کاملLong Minimal Zero - Sum Sequences in the Group C
A sequence in an additively written abelian group is called a minimal zero-sum sequence if its sum is the zero element of the group and none of its proper subsequences has sum zero. The structure of the longest minimal zero-sum sequences in the group C2 ⊕C2k is known. Their length is equal to 2k + 1. We characterize the minimal zero-sum sequences in C2 ⊕ C2k (k ≥ 3) with lengths at least 2�k/2�...
متن کاملOn Bialostocki’s Conjecture for Zero-sum Sequences
A finite sequence S of terms from an (additive) abelian group is said to have zero-sum if the sum of the terms of S is zero. In 1961 P. Erdős, A. Ginzburg and A. Ziv [3] proved that any sequence of 2n− 1 terms from an abelian group of order n contains an n-term zero-sum subsequence. This celebrated EGZ theorem is is an important result in combinatorial number theory and it has many different ge...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2014
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm135-2-4