[seqfan] Re: boxes in boxes
franktaw at netscape.net
franktaw at netscape.net
Sat Sep 26 01:20:37 CEST 2009
I'd skip the comment.
The correspondence is trivial. Each of your boxes is a node of one of
the trees in the forest. The label on the box is the number of points
associated with the node. One node is a child of another if the first
corresponding box is contained in the second.
So you're just describing the same thing with different words.
Franklin T. Adams-Watters
-----Original Message-----
From: Jon Wild <wild at music.mcgill.ca>
Dear seqfans,
Say you have a bunch of boxes, each labelled by an integer. Boxes can
go
inside other boxes. The sequence I was just thinking about is the
number
of ways I can give you a collection of boxes whose labels sum to n. For
n=3 for example, I can give you:
one box labelled 3;
one box labelled 2 and a separate box labelled 1;
a box labelled 2 with a box labelled 1 inside it;
a box labelled 1 with a box labelled 2 inside it;
three separate boxes labelled 1;
a box labelled 1 with another box labelled 1 inside it, plus a separate
box labelled 1;
a box labelled 1 with two separate boxes labelled 1 both inside it;
a box labelled 1 with a box labelled 1 inside it, with a third box
labelled 1 nested inside the second box.
That's 8 ways.
I checked by hand up to n=5 and got 1,3,8,24,71. Can someone confirm
that
this sequence is A052855, "Number of forests of rooted trees of
nonempty
sets with n points. (Each node is a set of 1 or more points.)"?
If so I'll add a comment, and if not I'll submit the sequence.
Jon
More information about the SeqFan
mailing list