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Rearrangement Distance Database

This is a database of the rearrangement distances of all permutations in the symmetric group. The data was generated by a program that implements a breadth-first search algorithm. The source code is available for download.
Instructions to search the rearrangement distance of a permutation
  • Enter a permutation in the text field.
    • The elements must be separated by a comma or a white space.
  • Choose a rearrangement model.
  • Check the "Solution" checkbox if you want to see a sequence of permutations that illustrates the transformation of identity permutation into the given one.
  • Press "Search" button and wait for server response.
Search Rearrangement Distance

Solution
The distance of permutation 1,2,3,4,5 is 0.
Instructions to recover a slice of the symmetric group
  • Enter the distance (d) in the first text field.
  • Enter the permutation size (n) in the second text field.
  • Choose a rearrangement model.
  • Press "Recover" button and wait for server response.
Recover Slice

(1 2 3 4 5)
Instructions to verify the rearrangement distance distribution
  • Choose a rearrangement model and wait for server response.
Rearrangement Distance Distribution

n
d12345678910111213
01111111111111
1136101521283645556678
2215521292664878201297195428313972
32553891563464211407246004820487758150707
421842539164456986322861362667715109733304457
5264816604169034101634143981361524060344997104
62211110536516865341431378981531167354920337
726352654030165849881988027571489090761
821733739001161596501622717751441
9242878220732301499706234
102102050116855950
112239756
122
Measures
nAverage DistanceD(n)T(n)L(n)
10000
20.5110
31.17211
41.75321
52.39431
63.04532
73.7642
84.38752
95.06853
105.76963
116.471073
127.181174
137.91284