## CNB9 More about the matrix M(E)

Hi to readers. All zero of them!

Recall from the previous Blog the matrix **M(E**) of entegers, which I produced from the starting enteger **1**v**1**, using the two operators **A(e)** and **F(e)**. I said that the Blog diverged from the realm of cycle-numbers, but not very far. Well, this Blog will put that right, and get us back to the cycle-number triangle. In several interesting ways.

Suppose I apply the coprimeness function kappa to each of the elements in M(E). All of the outputs will be 1, since we know that all enteger pairs in our Fibonacci and Arithmetic Progressions are coprime. So the resulting tree of **1**s will occur (embed) in matrix **C**.

Let us take all of these results **1**, and find where they occur in the cycle-number triangle **ÎșT(E**). We shall find that if we place a dot in each of the **1**s, and then join up the dots (in well-known play fashion!) we shall get a tree in the domain of **T**. * *I will show you the beginnings of this tree in the diagram below*.*

[to be continued, with the promised diagram]