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

Author

N. J. A. Sloane, Feb 19 2016

Keywords

• nonn
• base

Examples

			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
		

Links

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

Crossrefs

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