## CNB9 More about the matrix M(E)

August 28th, 2012

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 1v1, 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 1s will occur (embed) in matrix C.

Let us take all of these results 1, and find where they occur in the cycle-number triangle κT(E). We shall find that if we place a dot in each of the 1s, 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]