A240763 Preferential arrangements of 1, 2, 3, ... things in one-line notation, arranged lexicographically.

1, 11, 12, 21, 111, 112, 121, 122, 123, 132, 211, 212, 213, 221, 231, 312, 321, 1111, 1112, 1121, 1122, 1123, 1132, 1211, 1212, 1213, 1221, 1222, 1223, 1231, 1232, 1233, 1234, 1243, 1312, 1321, 1322, 1323, 1324, 1332, 1342, 1423, 1432, 2111, 2112, 2113, 2121, 2122, 2123, 2131, 2132, 2133, 2134, 2143, 2211, 2212

Offset

1,2

Comments

A preferential arrangement is like a permutation, except that ties are allowed. Preferential arrangements are also called ordered partitions. See A000670.

There are A000670(n) terms of length n.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..52609 (lists all preferential arrangements of <= 7 things).

N. J. A. Sloane, List of preferential arrangements on 1 thru 5 things, in human-readable notation [These are in a different order from those in the b-file]

Example

The preferential arrangement of 7 things given by
3=4 < 5 < 1=2=7 < 6
would be represented by
1 2 3 4 5 6 7
3 3 1 1 2 4 3
which in the compressed one-line notation is written 3311243. Obviously this compressed notation only works for fewer than 10 things. In the "human-readable" notation used in the a-file, this example would be written 34,5,127,6.
Thanks to Nathaniel Shar for suggesting the one-line notation.

Crossrefs

Cf. A000670, A239914, A217389, A030299 (an analogous sequence for permutations).

Sequence in context: A089185 A098754 A098752 * A231871 A192287 A084855

Adjacent sequences: A240760 A240761 A240762 * A240764 A240765 A240766

Keyword

nonn

Author

N. J. A. Sloane, Apr 12 2014

Status

approved