Title: Results on the Hilbert coefficients and reduction numbers,
Abstract: Let $(R,\frak{m})$ be a $d$-dimensional Cohen-Macaulay local ring, $I$ an
$\frak{m}$-primary ideal and $J$ a minimal reduction of $I$. In this paper we
study the independence of reduction ideals and the behavior of the higher
Hilbert coefficients. In addition, we give some examples in this regards.