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File:Weak orderings 3.svg

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Summary

Description

The Sloane's A000670(3) = 13 possible weak orderings on (or ordered set partitions of) a 3-element set

shown in the Cayley graph of S3 that looks like the permutohedron


Reading the permutation matrices by row gives the permutations in the Cayley graph, which also appear as labels a|b|c|d.
(Reading them by column gives the permutations in the permutohedron.)

There is also:
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last ⋅ first
This is:
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first ⋅ last
Date
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Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Permission
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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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Other versions
permutohedron with the same permutation matrices (representing the inverse permutations)
3
4

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Date/TimeThumbnailDimensionsUserComment
current00:12, 9 June 2013Thumbnail for version as of 00:12, 9 June 2013773 × 678 (99 KB)Watchducklayout
22:12, 26 May 2013Thumbnail for version as of 22:12, 26 May 2013948 × 752 (84 KB)Watchduck{{Information |Description ={{en|1=.}} |Source ={{own}} |Author ={{Mate2code}} |Date = |Permission = |other_versions = }} .

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