File:Symmetric group 4; permutation list.svg

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Summary

Description

All permutations of (1, 2, 3, 4) in reverse colexicographic order

Columns:

cycle notation
permutation matrix (active right)
row number of A055089 (factorial number converted to decimal), if the permutation is not self-conjugate the number of its inverse is shown below
one-line notation (row of array A055089), left inversion count
place-based inversion set
inversion number ( A034968, digit sum of factorial number and cardinality of inversion set)

List of the first 8! = 4320 permutations of 8 elements in the same order: https://oeis.org/A198380/a198380_1.txt

This SVG was created with Inkscape.

Source

Own work

Author

Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

Other versions

with permutations of (0, 1, 2, 3): File:Symmetric group 4; permutation list (0-based).svg

Licensing

I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	21:56, 21 August 2019	263 × 744 (1.42 MB)	Watchduck	gray fixed points
	15:29, 8 December 2016	263 × 744 (1.43 MB)	Watchduck	clockwise cycles (active postfix)
	00:59, 16 November 2016	263 × 744 (1.42 MB)	Watchduck	remove fixed points from cycles
	18:07, 13 November 2016	263 × 736 (1.53 MB)	Watchduck	details
	17:43, 7 October 2016	263 × 736 (1.45 MB)	Watchduck	layout
	17:10, 7 October 2016	281 × 744 (1.44 MB)	Watchduck	add matrices and cycle notation
	20:44, 8 November 2014	200 × 744 (1,014 KB)	Watchduck	change inversion sets
	21:18, 7 June 2012	200 × 744 (399 KB)	Watchduck	triangular inversion sets
	12:45, 6 October 2010	200 × 744 (1.25 MB)	Watchduck	stronger lines
	19:49, 5 October 2010	200 × 744 (1.26 MB)	Watchduck