[seqfan] Re: Infinite enumeration of finite partitions
franktaw at netscape.net
franktaw at netscape.net
Sat Feb 4 12:59:37 CET 2012
There are a number of enumerations of partitions in the OEIS.
Generally speaking, these are "tabf" sequences, showing the members of
the partitions rather than a single number encoding the entire
partition - as you have done in A194602.
The primary ones are A036036 (and A036037, which is the same
enumeration with the parts in a different order), and A080577. Others
include A080576, A112798, and A125106.
One enumeration of set partitions is in A120698.
Franklin T. Adams-Watters
-----Original Message-----
From: Tilman Piesk <vimarius at googlemail.com>
Hi seqfans,
I developed enumerations of all finite integer partitions and all finite
set partitions:
* Integer partitions:
http://commons.wikimedia.org/wiki/File:Partitions_of_10.svg#File
* Set partitions:
http://commons.wikimedia.org/wiki/File:Set_partitions_5;_lexicographical.svg#File
With enumeration I mean a bijection between all integers and all finite
partitions.
(I think seperate enumerations e.g. for partitions of a 4-element set
and
those of a 5-element set are not useful.)
Does anyone of you know if such enumerations already exist - possibly
better ones?
Applications:
* This sequence shows the cycle structure of the n-th finite permutation
using the enumeration of integer partitions:
http://oeis.org/A198380<https://oeis.org/A198380>
* The join and the meet table of the lattice of (all) set partitions
can be
represented by an infinite array of integers.
The same for the lattice of noncrossing partitions, etc.
Greetings,
Tilman Piesk
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