[seqfan] Infinite enumeration of finite partitions
Tilman Piesk
vimarius at googlemail.com
Thu Feb 2 02:16:11 CET 2012
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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