A268532 Decimal representation of permutations of lengths 1, 2, 3, ... arranged first by number of inversions and then lexicographically.

1, 12, 21, 123, 132, 213, 231, 312, 321, 1234, 1243, 1324, 2134, 1342, 1423, 2143, 2314, 3124, 1432, 2341, 2413, 3142, 3214, 4123, 2431, 3241, 3412, 4132, 4213, 3421, 4231, 4312, 4321, 12345, 12354, 12435, 13245, 21345, 12453

Offset

1,2

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..5913

David Consiglio, Jr., Python Program

Example

The 24 permutations of length 4 and their numbers of inversions:
1234 0
1243 1
1324 1
2134 1
1342 2
1423 2
2143 2
2314 2
3124 2
1432 3
2341 3
2413 3
3142 3
3214 3
4123 3
2431 4
3241 4
3412 4
4132 4
4213 4
3421 5
4231 5
4312 5
4321 6

Crossrefs

Cf. A000142 (n!), A030299 (in purely lexicographic order), A008302 (number of permutations with k inversions).

Sequence in context: A134514 A030299 A352991 * A260275 A001292 A292523

Adjacent sequences: A268529 A268530 A268531 * A268533 A268534 A268535

Keyword

nonn,base

Author

N. J. A. Sloane, Feb 19 2016

Status

approved