File:Weak orderings 3.svg

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:
left action
last ⋅ first
This is:
right action
first ⋅ last
Date
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Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
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Category:Self-published work#Weak%20orderings%203.svgCategory:PD-self#Weak%20orderings%203.svg
Other versions
permutohedron with the same permutation matrices (representing the inverse permutations)
3
4
Category:Weak orderings of a 3-set assigned to permutohedron faces Category:Permutation matrices of size 3
Category:PD-self Category:Permutation matrices of size 3 Category:Self-published work Category:Weak orderings of a 3-set assigned to permutohedron faces