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A240763
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Preferential arrangements of 1, 2, 3, ... things in one-line notation, arranged lexicographically.
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13
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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