Endofunctions by indegree

[Jonathan Post]

Okay, I've gone over my hand-drawings of the 47 endofunctions with n=5
nodes, and made a table of the indegree partitions. Might take too long, and
be too error prone, fdor me to type the whole table here.  So I'll skip to
column sums.

There are:
76 nodes of indegree 0,
106 nodes of indegree 1,
35 nodes of indegree 2,
14 nodes of indegree 3,
3 nodes of indegree 4,
1 node of indegree 5.
-------------------------------
235 total = 46*5, that checks.

Weighted Mean indegree:
(76*0 + 106*1 + 35*2 + 14*3 + 3*4 + 1*5)/47
= (106 + 70 + 42 + 12 + 5)/47 = 235/47 = 5, that checks.

The total number of preimages (predecessor nodes) is 159, since 159 + 76 =
235.

The number of 5-endofunctions with
max indegree of 0 is 0,
max indegree of 1 is 7,
max indegree of 2 is 22,
max indegree of 3 is 14,
max indegree of 4 is 3,
max indegree of 5 is 1.

Do those agree with your calculations, or should I take yet another look?


>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20061229/400ee89a/attachment-0002.htm>