کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4648632 | 1342421 | 2010 | 7 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Indexes of unsplittable minimal zero-sum sequences of length I(Cn)−1I(Cn)−1 Indexes of unsplittable minimal zero-sum sequences of length I(Cn)−1I(Cn)−1](/preview/png/4648632.png)
Let GG be a finite abelian group and S=g1⋯glS=g1⋯gl a minimal zero-sum sequence of elements in GG. We say that SS is unsplittable if there do not exist an element gi∈supp(S) and two elements x,y∈Gx,y∈G such that x+y=gix+y=gi and Sa−1xySa−1xy is a minimal zero-sum sequence as well. The notion of the index of a minimal zero-sum sequence in GG has been recently addressed in the mathematical literature (see Definition 1.1). Let I(Cn)I(Cn) be the minimal integer tt such that every minimal zero-sum sequence of at least tt elements in CnCn (the cyclic group of order nn) satisfies index(S)=1. In this paper, all the unsplittable minimal zero-sum sequences of length I(Cn)−1I(Cn)−1 are discovered and their indexes are computed. The results show that Conjecture 1.1 is true when nn is odd, and false when nn is even.
Journal: Discrete Mathematics - Volume 310, Issue 5, 6 March 2010, Pages 1127–1133