Id

Notation

Conducement

1

$\stackrel{2/3/o=1}{\overbrace{\left\{\mathbb{S}\right\}}}$

$\left\{\begin{array}{cc}1& \begin{array}{cc}7& \begin{array}{cc}19& \begin{array}{cc}37& \begin{array}{cc}61& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}1\\ 1\end{array}& \begin{array}{cc}\begin{array}{c}1\\ \begin{array}{c}1\\ 1\end{array}\end{array}& \cdots \end{array}\end{array}\end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}$

2

$\stackrel{1/2}{\overbrace{\left\{\mathbb{S}\right\}}}$

$\left\{\begin{array}{cc}1& \begin{array}{cc}6& \begin{array}{cc}12& \begin{array}{cc}18& \begin{array}{cc}24& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}1\\ 1\end{array}& \begin{array}{cc}\begin{array}{c}1\\ \begin{array}{c}1\\ 1\end{array}\end{array}& \cdots \end{array}\end{array}\end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}7& \begin{array}{cc}19& \begin{array}{cc}37& \begin{array}{cc}61& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}$

3

$\stackrel{0/1}{\overbrace{\left\{\mathbb{S}\right\}}}$

$\left\{\begin{array}{cc}1& \begin{array}{cc}5& \begin{array}{cc}6& \begin{array}{cc}6& \begin{array}{cc}6& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}1\\ 1\end{array}& \begin{array}{cc}\begin{array}{c}1\\ \begin{array}{c}1\\ 1\end{array}\end{array}& \cdots \end{array}\end{array}\end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}6& \begin{array}{cc}12& \begin{array}{cc}18& \begin{array}{cc}24& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}$

4

$\stackrel{\ker /0}{\overbrace{\left\{\mathbb{S}\right\}}}$

$\left\{\begin{array}{cc}1& \begin{array}{cc}4& \begin{array}{cc}1& \begin{array}{cc}0& \cdots \end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}1\\ 1\end{array}& \begin{array}{cc}\begin{array}{c}1\\ \begin{array}{c}1\\ 1\end{array}\end{array}& \cdots \end{array}\end{array}\end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}5& \begin{array}{cc}6& \begin{array}{cc}6& \begin{array}{cc}6& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}$

5

$\stackrel{0/\ker }{\overbrace{\left\{\mathbb{S}\right\}}}$

$\left\{\begin{array}{cc}1& \begin{array}{cc}3& \begin{array}{cc}-3& \begin{array}{cc}-1& \begin{array}{cc}0& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}1\\ 1\end{array}& \begin{array}{cc}\begin{array}{c}1\\ \begin{array}{c}1\\ 1\end{array}\end{array}& \cdots \end{array}\end{array}\end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}4& \begin{array}{cc}1& \begin{array}{cc}0& \cdots \end{array}\end{array}\end{array}\end{array}\right\}$

6

$\stackrel{0/-1}{\overbrace{\left\{\mathbb{S}\right\}}}$

$\left\{\begin{array}{cc}1& \begin{array}{cc}2& \begin{array}{cc}-6& \begin{array}{cc}2& \begin{array}{cc}1& 0\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}1\\ 1\end{array}& \begin{array}{cc}\begin{array}{c}1\\ \begin{array}{c}1\\ 1\end{array}\end{array}& \cdots \end{array}\end{array}\end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}3& \begin{array}{cc}-3& \begin{array}{cc}-1& 0\end{array}\end{array}\end{array}\end{array}\right\}$

7

$\stackrel{\ker /3}{\overbrace{\left\{\mathbb{S}\right\}}}$

$\stackrel{\text{Therestepsinoneandhencethescopeforgeneralisation}}{\overbrace{\left\{\begin{array}{cc}1& \begin{array}{cc}4& 1\end{array}\end{array}\right\}\oplus \left\{\begin{array}{ccc}\stackrel{T_1}{\overbrace{\left(\begin{array}{c}3\\ 0\end{array}\right)}}& \stackrel{T_2}{\overbrace{\left(\begin{array}{c}3\\ 0\end{array}\right)}}& \stackrel{T_3}{\overbrace{\left(\begin{array}{c}3\\ 0\end{array}\right)}}\\ & \left(\begin{array}{c}4\\ 1\end{array}\right)& \left(\begin{array}{c}4\\ 1\end{array}\right)\\ & & \left(\begin{array}{c}5\\ 2\end{array}\right)\end{array}\stackrel{\text{noticethemarchingoftheterms}}{\overbrace{\begin{array}{cccc}\left(\begin{array}{c}4\\ 1\end{array}\right)& \left(\begin{array}{c}5\\ 2\end{array}\right)& \left(\begin{array}{c}6\\ 3\end{array}\right)& \\ \left(\begin{array}{c}5\\ 2\end{array}\right)& \left(\begin{array}{c}6\\ 3\end{array}\right)& \left(\begin{array}{c}7\\ 4\end{array}\right)& \cdots \\ \left(\begin{array}{c}6\\ 3\end{array}\right)& \left(\begin{array}{c}7\\ 4\end{array}\right)& \left(\begin{array}{c}8\\ 5\end{array}\right)& \end{array}}}\right\}}}$

$=\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \cdots \end{array}\end{array}\end{array}\end{array}\right\}$

8

$\stackrel{k/3/o=2}{\overbrace{\left\{\mathbb{S}\right\}}}$

$\stackrel{\text{FourstepsinoneforsourceteratOrdinal2}}{\overbrace{\left\{\begin{array}{ccc}0& 8& \begin{array}{ccc}-5& 4& -1\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cccccc}\stackrel{0}{\overbrace{\left(\begin{array}{c}\\ \end{array}\right)}}& \stackrel{T_1}{\overbrace{\left(\begin{array}{c}3\\ 0\end{array}\right)}}& \stackrel{T_2}{\overbrace{\left(\begin{array}{c}3\\ 0\end{array}\right)}}& \stackrel{T_3}{\overbrace{\left(\begin{array}{c}3\\ 0\end{array}\right)}}& \left(\begin{array}{c}4\\ 1\end{array}\right)& \left(\begin{array}{c}5\\ 2\end{array}\right)\\ & & \left(\begin{array}{c}4\\ 1\end{array}\right)& \left(\begin{array}{c}4\\ 1\end{array}\right)& \left(\begin{array}{c}5\\ 2\end{array}\right)& \left(\begin{array}{c}6\\ 3\end{array}\right)\\ & & & \left(\begin{array}{c}5\\ 2\end{array}\right)& \left(\begin{array}{c}6\\ 3\end{array}\right)& \left(\begin{array}{c}7\\ 4\end{array}\right)\\ & & & & \left(\begin{array}{c}7\\ 4\end{array}\right)& \left(\begin{array}{c}8\\ 5\end{array}\right)\end{array}\cdots \right\}}}$

$=\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \cdots \end{array}\end{array}\end{array}\end{array}\right\}$