  In this article, we will investigate several new configurations in Ramsey
Theory, using the $\ostar_{l,k}$-operation on the set of integers, recently
introduced in \cite{key-4}. This operation is useful to study symmetric
structures in the set of integers, such as monochromatic configurations of the
form $\left\{ x,y,x+y+xy\right\} $ as one of its simplest case. In
\cite{key-4}, the author has studied more general symmetric structures. It has
been shown that the Hindman's Theorem, van der Waerden's Theorem, Deuber's
Theorem have their own symmetric versions. In this article we will explore
several new structures, including polynomial versions of these symmetric
structures and some of its variants. As a result, we get several new symmetric
polynomial configurations as well as new linear symmetric patterns. In the
final section, we will also introduce two new operations on the set of
non-negative integers $\mathbb{N}$, to obtain further new configurations.
