[seqfan] Re: Extension of A005646
franktaw at netscape.net
franktaw at netscape.net
Sat Dec 19 13:33:26 CET 2009
Oh, sorry; I see now that these are for unlabeled objects. I was
confused by Andrew's list of labeled partitions.
For n odd, you can avoid problems by always having the first part
bigger than the second; but for even n this doesn't always work. I
assume that you are doing, at some point, permutation of the objects to
see if two classifications are the same (presumably with
optimizations); I think you have to try flipping any balanced binary
partitions in that phase as well. (There are of course optimizations
to be made here; for example looking at the objects that occur alone,
put more of these in the first part if possible.)
-----
I would also like to see a triangle with T(n,k) being the number of
classifications of n objects using k binary partitions.
This starts:
1
0 1
0 0 1
0 0 1 2
0 0 0 3 3 (I think)
0 0 0 3 17 6 (from Andrew's list)
Franklin T. Adams-Watters
-----Original Message-----
From: franktaw at netscape.net
To avoid this, simply always include a particular number (0 if you
start with it, else 1) in the first part of each partition.
Franklin T. Adams-Watters
-----Original Message-----
From: Robert Munafo <mrob27 at gmail.com>
...
I suspect that I am treating two classifications as distinct when
complementing one of more of their constituent binary partitions would
make them equivalent, but not clear on how to detect or avoid.
...
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