| Anagram Index | A. 1 0 _ | Anagram |
|
If T is the table of all !n permutations of
order n arranged in lexical order (i.e., /:T
is i.!n), then k is said to be the
anagram index of the permutation k{T . A. applied to a cycle or direct permutation yields its anagram index: A. 0 3 2 1 is 5, as are A. 3 2 1 and A.<3 1 and A.0;2;3 1 . |
The expression k A. b permutes items of b by
the permutation of order #b whose anagram index is k .
|
(A. 0 3 2 1) , (A. <3 1)
5 5
A. |. i.45
119622220865480194561963161495657715064383733759999999999
<: ! 45x
119622220865480194561963161495657715064383733759999999999
tap=: i.@! A. i. NB. Table of all permutations
(tap 3);(/: tap 3);({/\ tap 3);(/:{/\ tap 3)
+-----+-----------+-----+-----------+
|0 1 2|0 1 2 3 4 5|0 1 2|0 1 5 2 4 3|
|0 2 1| |0 2 1| |
|1 0 2| |1 2 0| |
|1 2 0| |2 0 1| |
|2 0 1| |1 2 0| |
|2 1 0| |1 0 2| |
+-----+-----------+-----+-----------+
In particular, 1 A. b transposes the last two items
of b, and _1 A. b reverses
the list of items, and 3 A. b and 4 A. b rotate the
last three items of b. For example:
b=: 'ABCD'
(0 3 2 1{b);(0 3 2 1 C.b);((<3 1)C.b);(3 4 A.b)
+----+----+----+----+
|ADCB|ADCB|ADCB|ACDB|
| | | |ADBC|
+----+----+----+----+
(_19 5 A. b) ; (_19 |~ ! # b)
+----+-+
|ADCB|5|
|ADCB| |
+----+-+