Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001568
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[3,+,1] => [3,2,1] => [1,1,1]
 => [1,1]
 => 2
[3,-,1] => [3,2,1] => [1,1,1]
 => [1,1]
 => 2
[+,4,+,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 2
[-,4,+,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 2
[+,4,-,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 2
[-,4,-,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 2
[2,1,4,3] => [2,1,4,3] => [2,2]
 => [2]
 => 1
[2,4,1,3] => [2,4,1,3] => [2,2]
 => [2]
 => 1
[2,4,+,1] => [2,4,3,1] => [2,1,1]
 => [1,1]
 => 2
[2,4,-,1] => [2,4,3,1] => [2,1,1]
 => [1,1]
 => 2
[3,1,4,2] => [3,1,4,2] => [2,2]
 => [2]
 => 1
[3,+,1,+] => [3,2,1,4] => [2,1,1]
 => [1,1]
 => 2
[3,-,1,+] => [3,2,1,4] => [2,1,1]
 => [1,1]
 => 2
[3,+,1,-] => [3,2,1,4] => [2,1,1]
 => [1,1]
 => 2
[3,-,1,-] => [3,2,1,4] => [2,1,1]
 => [1,1]
 => 2
[3,+,4,1] => [3,2,4,1] => [2,1,1]
 => [1,1]
 => 2
[3,-,4,1] => [3,2,4,1] => [2,1,1]
 => [1,1]
 => 2
[3,4,1,2] => [3,4,1,2] => [2,2]
 => [2]
 => 1
[3,4,2,1] => [3,4,2,1] => [2,1,1]
 => [1,1]
 => 2
[4,1,+,2] => [4,1,3,2] => [2,1,1]
 => [1,1]
 => 2
[4,1,-,2] => [4,1,3,2] => [2,1,1]
 => [1,1]
 => 2
[4,+,1,3] => [4,2,1,3] => [2,1,1]
 => [1,1]
 => 2
[4,-,1,3] => [4,2,1,3] => [2,1,1]
 => [1,1]
 => 2
[4,+,+,1] => [4,2,3,1] => [2,1,1]
 => [1,1]
 => 2
[4,-,+,1] => [4,2,3,1] => [2,1,1]
 => [1,1]
 => 2
[4,+,-,1] => [4,2,3,1] => [2,1,1]
 => [1,1]
 => 2
[4,-,-,1] => [4,2,3,1] => [2,1,1]
 => [1,1]
 => 2
[4,3,1,2] => [4,3,1,2] => [2,1,1]
 => [1,1]
 => 2
[4,3,2,1] => [4,3,2,1] => [1,1,1,1]
 => [1,1,1]
 => 2
[+,+,5,+,3] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 2
[-,+,5,+,3] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 2
[+,-,5,+,3] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 2
[+,+,5,-,3] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 2
[-,-,5,+,3] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 2
[-,+,5,-,3] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 2
[+,-,5,-,3] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 2
[-,-,5,-,3] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 2
[+,3,2,5,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 1
[-,3,2,5,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 1
[+,3,5,2,4] => [1,3,5,2,4] => [3,2]
 => [2]
 => 1
[-,3,5,2,4] => [1,3,5,2,4] => [3,2]
 => [2]
 => 1
[+,3,5,+,2] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 2
[-,3,5,+,2] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 2
[+,3,5,-,2] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 2
[-,3,5,-,2] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 2
[+,4,2,5,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 1
[-,4,2,5,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 1
[+,4,+,2,+] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 2
[-,4,+,2,+] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 2
[+,4,-,2,+] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 2
Description
The smallest positive integer that does not appear twice in the partition.