Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000212
Mapping
St000212: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 0
[1,1]
 => 1
[3]
 => 0
[2,1]
 => 1
[1,1,1]
 => 1
[4]
 => 0
[3,1]
 => 0
[2,2]
 => 1
[2,1,1]
 => 2
[1,1,1,1]
 => 1
[5]
 => 0
[4,1]
 => 0
[3,2]
 => 1
[3,1,1]
 => 1
[2,2,1]
 => 3
[2,1,1,1]
 => 3
[1,1,1,1,1]
 => 1
[6]
 => 0
[5,1]
 => 0
[4,2]
 => 0
[4,1,1]
 => 0
[3,3]
 => 1
[3,2,1]
 => 5
[3,1,1,1]
 => 3
[2,2,2]
 => 2
[2,2,1,1]
 => 6
[2,1,1,1,1]
 => 4
[1,1,1,1,1,1]
 => 1
[7]
 => 0
[6,1]
 => 0
[5,2]
 => 0
[5,1,1]
 => 0
[4,3]
 => 1
[4,2,1]
 => 2
[4,1,1,1]
 => 1
[3,3,1]
 => 5
[3,2,2]
 => 6
[3,2,1,1]
 => 14
[3,1,1,1,1]
 => 6
[2,2,2,1]
 => 8
[2,2,1,1,1]
 => 10
[2,1,1,1,1,1]
 => 5
[1,1,1,1,1,1,1]
 => 1
[8]
 => 0
[7,1]
 => 0
[6,2]
 => 0
[6,1,1]
 => 0
[5,3]
 => 0
[5,2,1]
 => 0
Description
The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. Summing over all partitions of $n$ yields the sequence $$1, 1, 1, 2, 4, 9, 22, 59, 170, 516, 1658, \dots$$ which is [[oeis:A237770]]. The references in this sequence of the OEIS indicate a connection with Baxter permutations.
Matching statistic: St001491
Mapping
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 2% ●values known / values provided: 11%●distinct values known / distinct values provided: 2%
Values
[1]
 => []
 => []
 => => ? = 1
[2]
 => []
 => []
 => => ? = 0
[1,1]
 => [1]
 => [1,0]
 => 10 => 1
[3]
 => []
 => []
 => => ? = 0
[2,1]
 => [1]
 => [1,0]
 => 10 => 1
[1,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[4]
 => []
 => []
 => => ? ∊ {0,2}
[3,1]
 => [1]
 => [1,0]
 => 10 => 1
[2,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[2,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[1,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? ∊ {0,2}
[5]
 => []
 => []
 => => ? ∊ {0,1,3,3}
[4,1]
 => [1]
 => [1,0]
 => 10 => 1
[3,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[3,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[2,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? ∊ {0,1,3,3}
[2,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? ∊ {0,1,3,3}
[1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 11010100 => ? ∊ {0,1,3,3}
[6]
 => []
 => []
 => => ? ∊ {0,0,0,2,3,4,5,6}
[5,1]
 => [1]
 => [1,0]
 => 10 => 1
[4,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[4,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[3,3]
 => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? ∊ {0,0,0,2,3,4,5,6}
[3,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? ∊ {0,0,0,2,3,4,5,6}
[3,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? ∊ {0,0,0,2,3,4,5,6}
[2,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => 111000 => ? ∊ {0,0,0,2,3,4,5,6}
[2,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? ∊ {0,0,0,2,3,4,5,6}
[2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 11010100 => ? ∊ {0,0,0,2,3,4,5,6}
[1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1101010100 => ? ∊ {0,0,0,2,3,4,5,6}
[7]
 => []
 => []
 => => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[6,1]
 => [1]
 => [1,0]
 => 10 => 1
[5,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[5,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[4,3]
 => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[4,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[4,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[3,3,1]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[3,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => 111000 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[3,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 11010100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[2,2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 11100100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[2,2,1,1,1]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1101010100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 110101010100 => ? ∊ {0,0,0,1,2,5,5,6,6,8,10,14}
[8]
 => []
 => []
 => => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[7,1]
 => [1]
 => [1,0]
 => 10 => 1
[6,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[6,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[5,3]
 => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[5,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[5,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[4,4]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[4,3,1]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[4,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => 111000 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[4,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[4,1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 11010100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[3,3,2]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[3,3,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1010110100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[3,2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 11100100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[3,2,1,1,1]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[3,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1101010100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[2,2,2,2]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => 11110000 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[2,2,2,1,1]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => 1110010100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[2,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => 101101010100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 110101010100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => 11010101010100 => ? ∊ {0,0,0,0,0,0,4,6,6,6,8,10,10,11,15,16,18,28,30}
[9]
 => []
 => []
 => => ? ∊ {0,0,0,0,0,0,1,2,3,3,6,7,7,10,15,21,23,24,28,33,34,35,37,40,54,55,76}
[8,1]
 => [1]
 => [1,0]
 => 10 => 1
[7,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[7,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[6,3]
 => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? ∊ {0,0,0,0,0,0,1,2,3,3,6,7,7,10,15,21,23,24,28,33,34,35,37,40,54,55,76}
[9,1]
 => [1]
 => [1,0]
 => 10 => 1
[8,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[8,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[10,1]
 => [1]
 => [1,0]
 => 10 => 1
[9,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[9,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[11,1]
 => [1]
 => [1,0]
 => 10 => 1
[10,2]
 => [2]
 => [1,0,1,0]
 => 1010 => 0
[10,1,1]
 => [1,1]
 => [1,1,0,0]
 => 1100 => 1
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let $A_n=K[x]/(x^n)$. We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.