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File:Inversion set and vector of a permutation.svg

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Description

Example of inversions of a permutation

The example permutation (4,1,5,2,6,3) has the left inversion count (0,1,0,2,0,3)
and the inversion set { (1,2) , (1,4),(3,4) , (1,6),(3,6),(5,6) }.
The left inversion count converted to decimal is 373 - the permutation's reverse colexicographic rank.

(This permutation is also shown in this array.)


The inversion set contains 6 of the = 15 2-subsets of a 6-set.

The triangle is ordered like the square array Sloane's A018900 (compare this triangle).
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Watchduck
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Date/TimeThumbnailDimensionsUserComment
current13:14, 11 March 2017Thumbnail for version as of 13:14, 11 March 2017553 × 777 (186 KB)WatchduckCorrect terminology: little-endian factorial number --> left inversion count
20:17, 15 December 2016Thumbnail for version as of 20:17, 15 December 2016553 × 777 (196 KB)WatchduckCorrect terminology: inversion vector --> little-endian factorial number
14:33, 17 June 2012Thumbnail for version as of 14:33, 17 June 2012553 × 777 (168 KB)Watchduck{{Information |Description=Inversion (discrete mathematics) The example permutation '''(5,2,1,4,6,3)''' has the inversion vector <font color=red>(0,1,0,2,0,3)</font> and the inversion set <font color=red>'''{'''...

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