Long zero-free sequences in finite cyclic groups
نویسندگان
چکیده
منابع مشابه
Long zero-free sequences in finite cyclic groups
A sequence in an additively written abelian group is called zero-free if each of its nonempty subsequences has sum different from the zero element of the group. The article determines the structure of the zero-free sequences with lengths greater than n/2 in the additive group Zn of integers modulo n. The main result states that for each zero-free sequence (ai) l i=1 of length l > n/2 in Zn ther...
متن کاملLong n-zero-free sequences in finite cyclic groups
A sequence in the additive group Zn of integers modulo n is called n-zero-free if it does not contain subsequences with length n and sum zero. The article characterizes the n-zero-free sequences in Zn of length greater than 3n/2−1. The structure of these sequences is completely determined, which generalizes a number of previously known facts. The characterization cannot be extended in the same ...
متن کاملMinimal Zero Sequences of Finite Cyclic Groups
If G is a finite Abelian group, let MZS(G, k) denote the set of minimal zero sequences of G of length k. In this paper we investigate the structure of the elements of this set, and the cardinality of the set itself. We do this for the class of groups G = Zn for k both small (k ≤ 4) and large (k > 2n 3 ).
متن کاملZero Sums in Finite Cyclic Groups
Let Cn be the cyclic group of n elements, and let S = (a1, · · · , ak) be a sequence of elements in Cn. We say that S is a zero sequence if ∑k i=1 ai = 0 and that S is a minimal zero-sequence if S is a zero sequence and S contains no proper zero subsequence. In this paper we prove, among other results, that if S is a minimal zero sequence of elements in Cn and |S| ≥ n − [ 3 ] + 1, then there ex...
متن کاملWeighted Sequences in Finite Cyclic Groups∗
Let p > 7 be a prime, let G = Z/pZ, and let S1 = ∏p i=1 gi and S2 = ∏p i=1 hi be two sequences with terms from G. Suppose that the maximum multiplicity of a term from either S1 or S2 is at most 2p+1 5 . Then we show that, for each g ∈ G, there exists a permutation σ of 1, 2, . . . , p such that g = ∑p i=1(gi · hσ(i)). The question is related to a conjecture of A. Bialostocki concerning weighted...
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: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.01.012