67 research outputs found
Davenport constant with weights
For the cyclic group and any non-empty
. We define the Davenport constant of with weight ,
denoted by , to be the least natural number such that for any
sequence with , there exists a non-empty
subsequence and such that
. Similarly, we define the constant to be
the least such that for all sequences with
, there exist indices , and with . In the present paper, we show that
. This solve the problem raised by Adhikari and Rath
\cite{ar06}, Adhikari and Chen \cite{ac08}, Thangadurai \cite{th07} and
Griffiths \cite{gr08}.Comment: 6page
Further Results on Permutation Polynomials over Finite Fields
Permutation polynomials are an interesting subject of mathematics and have
applications in other areas of mathematics and engineering. In this paper, we
develop general theorems on permutation polynomials over finite fields. As a
demonstration of the theorems, we present a number of classes of explicit
permutation polynomials on \gf_q
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