

A240763


Preferential arrangements of 1, 2, 3, ... things in oneline notation, arranged lexicographically.


13



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
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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



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 oneline notation is written 3311243. Obviously this compressed notation only works for fewer than 10 things. In the "humanreadable" notation used in the afile, this example would be written 34,5,127,6.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



