Definition ($(m,p,c)$-set). An $(m,p,c)$-set $S\subseteq \mathbb{N}$ ($m$ the number of generators, $p$ the range of coefficients, $c$ the leading coefficient) with $x_1,x_2,\dots ,x_m$ is the set of the following form:

$$S=\left\{\sum _{i=1}^m{\lambda }_i{x}_i:\exists j,{\lambda }_j=c\text{ and }\forall i<j,{\lambda }_i=0,\text{ and }\forall k>j,{\lambda }_k\in [-p,p]\right\}$$

$$\begin{array}{llll}\hfill c{x}_1+{\lambda }_2{x}_2+{\lambda }_3{x}_3+\cdots +{\lambda }_m{x}_m& {\lambda }_i\in [-p,p]& \hfill & \\ \hfill c{x}_2+{\lambda }_3{x}_3+\cdots +{\lambda }_m{x}_m& {\lambda }_i\in [-p,p]& \hfill & \\ \hfill ⋮& & \hfill & \\ \hfill c_m{x}_m& {\lambda }_i\in [-p,p]& \hfill & \end{array}$$ We call these the rows of the $(m,p,c)$-set.