A056019 - Self-inverse infinite permutation which shows the position of each finite permutation's inverse permutation in A055089
programming/2007-September/008062 inverse permutation vector
pr=: 3 : 0 NB. PermRevLexRank - unfinished sketch
r=. - {.y
for_j.>:i.-<:#y do.
r=. r + (j - j{y) * !x:j
y=. ( (j{y) (]-<) (j-1){.y ) , j}.y
end.
r
)Ai=: A.@/:@(A. i.)~"0 4 Ai i.!4 0 1 2 4 3 5 6 7 12 18 13 19 8 10 14 20 16 22 9 11 15 21 17 23
viewmat |:(5 Ai i.!5) A. i.5
,.|:&.> (2 3 4 #: i.!4) ; (4 3 2 1 #: i.!4) ; (4 Ai i.!4) A. i.4 +-----------------------------------------------+ |0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 0 1 1 1 1 2 2 2 2 0 0 0 0 1 1 1 1 2 2 2 2| |0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3| +-----------------------------------------------+ |0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3| |0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2| |0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1| |0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0| +-----------------------------------------------+ |0 0 0 0 0 0 1 1 2 3 2 3 1 1 2 3 2 3 1 1 2 3 2 3| |1 1 2 3 2 3 0 0 0 0 0 0 2 3 1 1 3 2 2 3 1 1 3 2| |2 3 1 1 3 2 2 3 1 1 3 2 0 0 0 0 0 0 3 2 3 2 1 1| |3 2 3 2 1 1 3 2 3 2 1 1 3 2 3 2 1 1 0 0 0 0 0 0| +-----------------------------------------------+
0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 (]+<:) 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2 1 1 2 2 3 3 0 0 2 2 3 3 0 0 1 1 3 3 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2 (]+<:) 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 (]+<:) 1 2 0 2 0 1 1 2 0 2 0 1 1 2 0 2 0 1 1 2 0 2 0 1 2 3 1 3 1 2 2 3 0 3 0 2 1 3 0 3 0 1 1 2 0 2 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 (]+<:) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1 2 2 (]+<:) 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 (]+<:) 2 1 2 0 1 0 2 1 2 0 1 0 2 1 2 0 1 0 2 1 2 0 1 0 3 2 3 1 2 1 3 2 3 0 2 0 3 1 3 0 1 0 2 1 2 0 1 0
7 8 A. 'abcd'
badc
bcad
7 8 ((] + <:)/\"1@(#:~ (- i.)@#) { ]) 'abcd'
badc
bcad