Xiangneng Zeng

A note on linear permutation polynomials

Abstract Kai Zhou (2008) [8] gave an explicit representation of the class of linear permutation polynomials and computed the number of them. In this paper, we give a simple proof of the above results.

Indexes of long zero-sum sequences over cyclic groups

Let G be a cyclic group of order n , and let S ? F ( G ) be a zero-sum sequence of length | S | ? 2 ? n / 2 ? + 2 . Suppose that S can be decomposed into a product of at most two minimal zero-sum sequences. Then there exists some g ? G such that S = ( n 1 g ) ? ( n 2 g ) ? ? ? ( n | S | g ) , where n i ? 1 , n ] for all i ? 1 , | S | ] and n 1 + n 2 + ? + n | S | = 2 n . And we also generalize the above result to long zero-sum sequences which can be decomposed into at most k ? 3 minimal zero-sum sequences.

Normal sequences over finite abelian groups

In this note, we obtain the structure of short normal sequences over a finite abelian p-group or a finite abelian group of rank two, thus answering positively a conjecture of Gao and Zhuang for various groups. The results obtained here improve all known results on this conjecture.

Long minimal zero-sum sequences over a finite subset of Z

Abstract Let G be an abelian group (written additively), X be a subset of G and S be a minimal zero-sum sequence over X . S is called unsplittable in X if there do not exist an element g in S and two elements x , y in X such that g = x + y and the new sequence S g − 1 x y is still a minimal zero-sum sequence. In this paper, we mainly investigate the case when G = Z and X = 〚 − m , n 〛 with m , n ∈ N . We obtain the structure of unsplittable minimal zero-sum sequences of length at least n + ⌊ m ∕ 2 ⌋ + 2 provided that n ≥ m 2 ∕ 2 − 1 and m ≥ 6 . As a corollary, the Davenport constant D ( 〚 − m , n 〛 ) is determined when n ≥ m 2 ∕ 2 − 1 . The Davenport constant D ( X ) for a general set X ⊂ Z is also discussed.