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  • Jesse Sakari Hyttinen

An example in tree generation - Jesse Hyttinen

Updated: Apr 21, 2021


Hi and welcome to the Matladpi blog! In this post I will show an example in tree generation for a rooted trees case.

Let v = 5. There are 9 rooted trees with 5 vertices:

5 = 1 + 1×4 •= 1 + 2 + 1×2

                     •= 1 + 2×2

•= 1 + 3 + 1

•= 1 + (1 + 2) + 1

•= 1 + 4

•= 1 + (1 + 2 + 1)

•= 1 + (1 + 3)

•= 1 + (1 + (1 + 2))

The largest branch increases in size when the column is switched to a new one. For example, in the second column, the largest branch is 2, and then, when the column is switched to the next one, the largest branch is 3. This behaviour is purposefully created so that the structure would be more pleasant and convenient to be read.

The stacking of number two in the second column is also due to the behaviour of the tree generation algorithm. The order is lexicographic, and the forms of the branches will be gone through before the stacking would take place. Notice that also other branches than 2 can stack.

For example, for a rooted tree sum form 

1 + 3 + 1×4

, the following forms would follow if tga would be used:

1 + 3 + 1×4

•= 1 + (1 + 2) + 1×4

•= 1 + 3 + 2 + 1×2

•= 1 + (1 + 2) + 2 + 1×2

•= 1 + 3 + 2×2

•= 1 + (1 + 2) + 2×2

•= 1 + 3×2 + 1

•= 1 + (1 + 2) + 3 + 1

•= 1 + (1 + 2)×2 + 1

And then, the column would change. Njäf! said.

I am Jesse Sakari Hyttinen and I will see you in the next post!

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