Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000057
(load all 7 compositions to match this statistic)
Mapping
Mp00112: Set partitions —complement⟶ Set partitions
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
St000057: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => {{1}}
 => [[1]]
 => 0
{{1,2}}
 => {{1,2}}
 => [[1,2]]
 => 0
{{1},{2}}
 => {{1},{2}}
 => [[1],[2]]
 => 0
{{1,2,3}}
 => {{1,2,3}}
 => [[1,2,3]]
 => 0
{{1,2},{3}}
 => {{1},{2,3}}
 => [[1,3],[2]]
 => 0
{{1,3},{2}}
 => {{1,3},{2}}
 => [[1,3],[2]]
 => 0
{{1},{2,3}}
 => {{1,2},{3}}
 => [[1,2],[3]]
 => 1
{{1},{2},{3}}
 => {{1},{2},{3}}
 => [[1],[2],[3]]
 => 0
{{1,2,3,4}}
 => {{1,2,3,4}}
 => [[1,2,3,4]]
 => 0
{{1,2,3},{4}}
 => {{1},{2,3,4}}
 => [[1,3,4],[2]]
 => 0
{{1,2,4},{3}}
 => {{1,3,4},{2}}
 => [[1,3,4],[2]]
 => 0
{{1,2},{3,4}}
 => {{1,2},{3,4}}
 => [[1,2],[3,4]]
 => 1
{{1,2},{3},{4}}
 => {{1},{2},{3,4}}
 => [[1,4],[2],[3]]
 => 0
{{1,3,4},{2}}
 => {{1,2,4},{3}}
 => [[1,2,4],[3]]
 => 1
{{1,3},{2,4}}
 => {{1,3},{2,4}}
 => [[1,3],[2,4]]
 => 0
{{1,3},{2},{4}}
 => {{1},{2,4},{3}}
 => [[1,4],[2],[3]]
 => 0
{{1,4},{2,3}}
 => {{1,4},{2,3}}
 => [[1,3],[2,4]]
 => 0
{{1},{2,3,4}}
 => {{1,2,3},{4}}
 => [[1,2,3],[4]]
 => 2
{{1},{2,3},{4}}
 => {{1},{2,3},{4}}
 => [[1,3],[2],[4]]
 => 1
{{1,4},{2},{3}}
 => {{1,4},{2},{3}}
 => [[1,4],[2],[3]]
 => 0
{{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => [[1,3],[2],[4]]
 => 1
{{1},{2},{3,4}}
 => {{1,2},{3},{4}}
 => [[1,2],[3],[4]]
 => 2
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => [[1],[2],[3],[4]]
 => 0
{{1},{2,3,4,5}}
 => {{1,2,3,4},{5}}
 => [[1,2,3,4],[5]]
 => 3
{{1},{2,3,4},{5}}
 => {{1},{2,3,4},{5}}
 => [[1,3,4],[2],[5]]
 => 2
{{1},{2,3,5},{4}}
 => {{1,3,4},{2},{5}}
 => [[1,3,4],[2],[5]]
 => 2
{{1},{2,3},{4,5}}
 => {{1,2},{3,4},{5}}
 => [[1,2],[3,4],[5]]
 => 3
{{1},{2,3},{4},{5}}
 => {{1},{2},{3,4},{5}}
 => [[1,4],[2],[3],[5]]
 => 1
{{1},{2,4,5},{3}}
 => {{1,2,4},{3},{5}}
 => [[1,2,4],[3],[5]]
 => 3
{{1},{2,4},{3,5}}
 => {{1,3},{2,4},{5}}
 => [[1,3],[2,4],[5]]
 => 2
{{1},{2,4},{3},{5}}
 => {{1},{2,4},{3},{5}}
 => [[1,4],[2],[3],[5]]
 => 1
{{1},{2,5},{3,4}}
 => {{1,4},{2,3},{5}}
 => [[1,3],[2,4],[5]]
 => 2
{{1},{2},{3,4,5}}
 => {{1,2,3},{4},{5}}
 => [[1,2,3],[4],[5]]
 => 4
{{1},{2},{3,4},{5}}
 => {{1},{2,3},{4},{5}}
 => [[1,3],[2],[4],[5]]
 => 2
{{1},{2,5},{3},{4}}
 => {{1,4},{2},{3},{5}}
 => [[1,4],[2],[3],[5]]
 => 1
{{1},{2},{3,5},{4}}
 => {{1,3},{2},{4},{5}}
 => [[1,3],[2],[4],[5]]
 => 2
{{1},{2},{3},{4,5}}
 => {{1,2},{3},{4},{5}}
 => [[1,2],[3],[4],[5]]
 => 3
{{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => [[1],[2],[3],[4],[5]]
 => 0
Description
The Shynar inversion number of a standard tableau. Shynar's inversion number is the number of inversion pairs in a standard Young tableau, where an inversion pair is defined as a pair of integers (x,y) such that y > x and y appears strictly southwest of x in the tableau.
Matching statistic: St001867
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001867: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => [1] => 0
{{1,2}}
 => [2,1] => [2,1] => [2,1] => 0
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,1,2] => [3,1,2] => 0
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,1,3] => 0
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => [3,2,1] => 0
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [3,1,2,4] => [3,1,2,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => [4,1,3,2] => 0
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [4,2,1,3] => [4,2,1,3] => 1
{{1,3},{2,4}}
 => [3,4,1,2] => [3,4,1,2] => [3,4,1,2] => 0
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => [4,2,3,1] => 0
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 2
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => 3
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => 2
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,5,2,4,3] => [1,5,2,4,3] => 2
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 3
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,5,3,2,4] => [1,5,3,2,4] => 3
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,4,5,2,3] => [1,4,5,2,3] => 2
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 2
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,5,3,4] => [1,2,5,3,4] => 4
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,5,3,4,2] => [1,5,3,4,2] => 1
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 2
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 3
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
Description
The number of alignments of type EN of a signed permutation. An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold: * $-i < 0 < -\pi(i) < \pi(j) < j$ * $i \leq\pi(i) < \pi(j) < j$.
Matching statistic: St000589
(load all 10 compositions to match this statistic)
Mapping
St000589: Set partitions ⟶ ℤResult quality: 97% ●values known / values provided: 97%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => ? = 0
{{1,2}}
 => 0
{{1},{2}}
 => 0
{{1,2,3}}
 => 0
{{1,2},{3}}
 => 0
{{1,3},{2}}
 => 0
{{1},{2,3}}
 => 1
{{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => 0
{{1,2,4},{3}}
 => 0
{{1,2},{3,4}}
 => 1
{{1,2},{3},{4}}
 => 0
{{1,3,4},{2}}
 => 1
{{1,3},{2,4}}
 => 0
{{1,3},{2},{4}}
 => 0
{{1,4},{2,3}}
 => 0
{{1},{2,3,4}}
 => 2
{{1},{2,3},{4}}
 => 1
{{1,4},{2},{3}}
 => 0
{{1},{2,4},{3}}
 => 1
{{1},{2},{3,4}}
 => 2
{{1},{2},{3},{4}}
 => 0
{{1},{2,3,4,5}}
 => 3
{{1},{2,3,4},{5}}
 => 2
{{1},{2,3,5},{4}}
 => 2
{{1},{2,3},{4,5}}
 => 3
{{1},{2,3},{4},{5}}
 => 1
{{1},{2,4,5},{3}}
 => 3
{{1},{2,4},{3,5}}
 => 2
{{1},{2,4},{3},{5}}
 => 1
{{1},{2,5},{3,4}}
 => 2
{{1},{2},{3,4,5}}
 => 4
{{1},{2},{3,4},{5}}
 => 2
{{1},{2,5},{3},{4}}
 => 1
{{1},{2},{3,5},{4}}
 => 2
{{1},{2},{3},{4,5}}
 => 3
{{1},{2},{3},{4},{5}}
 => 0
Description
The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block.
Matching statistic: St001857
(load all 7 compositions to match this statistic)
Mapping
Mp00220: Set partitions —Yip⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 40%
Values
{{1}}
 => {{1}}
 => [1] => [1] => 0
{{1,2}}
 => {{1,2}}
 => [2,1] => [2,1] => 0
{{1},{2}}
 => {{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => {{1,2,3}}
 => [2,3,1] => [2,3,1] => 0
{{1,2},{3}}
 => {{1,2},{3}}
 => [2,1,3] => [2,1,3] => 0
{{1,3},{2}}
 => {{1},{2,3}}
 => [1,3,2] => [1,3,2] => 0
{{1},{2,3}}
 => {{1,3},{2}}
 => [3,2,1] => [3,2,1] => 1
{{1},{2},{3}}
 => {{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => {{1,2,3,4}}
 => [2,3,4,1] => [2,3,4,1] => ? = 0
{{1,2,3},{4}}
 => {{1,2,3},{4}}
 => [2,3,1,4] => [2,3,1,4] => ? = 0
{{1,2,4},{3}}
 => {{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => ? = 0
{{1,2},{3,4}}
 => {{1,2,4},{3}}
 => [2,4,3,1] => [2,4,3,1] => ? = 1
{{1,2},{3},{4}}
 => {{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => ? = 0
{{1,3,4},{2}}
 => {{1},{2,3,4}}
 => [1,3,4,2] => [1,3,4,2] => ? = 1
{{1,3},{2,4}}
 => {{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => ? = 0
{{1,3},{2},{4}}
 => {{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => ? = 0
{{1,4},{2,3}}
 => {{1,3},{2,4}}
 => [3,4,1,2] => [3,4,1,2] => ? = 0
{{1},{2,3,4}}
 => {{1,3,4},{2}}
 => [3,2,4,1] => [3,2,4,1] => ? = 2
{{1},{2,3},{4}}
 => {{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => ? = 1
{{1,4},{2},{3}}
 => {{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => ? = 0
{{1},{2,4},{3}}
 => {{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => ? = 1
{{1},{2},{3,4}}
 => {{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => ? = 2
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => ? = 0
{{1},{2,3,4,5}}
 => {{1,3,4,5},{2}}
 => [3,2,4,5,1] => [3,2,4,5,1] => ? = 3
{{1},{2,3,4},{5}}
 => {{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [3,2,4,1,5] => ? = 2
{{1},{2,3,5},{4}}
 => {{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [3,5,1,4,2] => ? = 2
{{1},{2,3},{4,5}}
 => {{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [3,2,5,4,1] => ? = 3
{{1},{2,3},{4},{5}}
 => {{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [3,2,1,4,5] => ? = 1
{{1},{2,4,5},{3}}
 => {{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,4,3,5,2] => ? = 3
{{1},{2,4},{3,5}}
 => {{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [5,4,3,2,1] => ? = 2
{{1},{2,4},{3},{5}}
 => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => ? = 1
{{1},{2,5},{3,4}}
 => {{1,4},{2,5},{3}}
 => [4,5,3,1,2] => [4,5,3,1,2] => ? = 2
{{1},{2},{3,4,5}}
 => {{1,4,5},{2},{3}}
 => [4,2,3,5,1] => [4,2,3,5,1] => ? = 4
{{1},{2},{3,4},{5}}
 => {{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => [4,2,3,1,5] => ? = 2
{{1},{2,5},{3},{4}}
 => {{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,5,4,3] => ? = 1
{{1},{2},{3,5},{4}}
 => {{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,5,3,4,2] => ? = 2
{{1},{2},{3},{4,5}}
 => {{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [5,2,3,4,1] => ? = 3
{{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
Description
The number of edges in the reduced word graph of a signed permutation. The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.
Matching statistic: St000102
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
St000102: Semistandard tableaux ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 20%
Values
{{1}}
 => [1] => [[1]]
 => [[1]]
 => 0
{{1,2}}
 => [2,1] => [[0,1],[1,0]]
 => [[1,2],[2]]
 => 0
{{1},{2}}
 => [1,2] => [[1,0],[0,1]]
 => [[1,1],[2]]
 => 0
{{1,2,3}}
 => [2,3,1] => [[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => ? = 0
{{1,2},{3}}
 => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => ? = 0
{{1,3},{2}}
 => [3,2,1] => [[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => ? = 0
{{1},{2,3}}
 => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => ? = 1
{{1},{2},{3}}
 => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => ? = 0
{{1,2,3,4}}
 => [2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,4],[2,2,4],[3,4],[4]]
 => ? = 0
{{1,2,3},{4}}
 => [2,3,1,4] => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,3],[2,2,3],[3,3],[4]]
 => ? = 0
{{1,2,4},{3}}
 => [2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,4],[2,3,4],[3,4],[4]]
 => ? = 0
{{1,2},{3,4}}
 => [2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,2],[3,4],[4]]
 => ? = 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,2],[3,3],[4]]
 => ? = 0
{{1,3,4},{2}}
 => [3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,4],[2,2,4],[3,4],[4]]
 => ? = 1
{{1,3},{2,4}}
 => [3,4,1,2] => [[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,3],[2,3,4],[3,4],[4]]
 => ? = 0
{{1,3},{2},{4}}
 => [3,2,1,4] => [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,3],[2,2,3],[3,3],[4]]
 => ? = 0
{{1,4},{2,3}}
 => [4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,4],[2,3,4],[3,4],[4]]
 => ? = 0
{{1},{2,3,4}}
 => [1,3,4,2] => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,1],[2,2,4],[3,4],[4]]
 => ? = 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,3],[3,3],[4]]
 => ? = 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,4],[2,3,4],[3,4],[4]]
 => ? = 0
{{1},{2,4},{3}}
 => [1,4,3,2] => [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,1],[2,3,4],[3,4],[4]]
 => ? = 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,2],[3,4],[4]]
 => ? = 2
{{1},{2},{3},{4}}
 => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,2],[3,3],[4]]
 => ? = 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]
 => ? = 3
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]]
 => ? = 2
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]
 => ? = 2
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
 => ? = 3
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
 => ? = 1
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]
 => ? = 3
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]
 => ? = 2
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ? = 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
 => [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]
 => ? = 2
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]]
 => ? = 4
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
 => ? = 2
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]
 => [[1,1,1,1,1],[2,3,3,5],[3,4,5],[4,5],[5]]
 => ? = 1
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]]
 => ? = 2
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
 => ? = 3
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
 => ? = 0
Description
The charge of a semistandard tableau.
Matching statistic: St001964
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 20%
Values
{{1}}
 => [1] => ([(0,1)],2)
 => ([(0,1)],2)
 => 0
{{1,2}}
 => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
{{1},{2}}
 => [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
{{1,2,3}}
 => [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 0
{{1,2},{3}}
 => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 0
{{1,3},{2}}
 => [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0
{{1},{2,3}}
 => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
{{1},{2},{3}}
 => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0
{{1,2,3,4}}
 => [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0
{{1,2,3},{4}}
 => [2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 0
{{1,2,4},{3}}
 => [2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 0
{{1,2},{3,4}}
 => [2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ? = 1
{{1,2},{3},{4}}
 => [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0
{{1,3,4},{2}}
 => [3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 1
{{1,3},{2,4}}
 => [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ? = 0
{{1,3},{2},{4}}
 => [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0
{{1,4},{2,3}}
 => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 0
{{1},{2,3,4}}
 => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 2
{{1},{2,3},{4}}
 => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 1
{{1,4},{2},{3}}
 => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0
{{1},{2,4},{3}}
 => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 1
{{1},{2},{3,4}}
 => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 2
{{1},{2},{3},{4}}
 => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ? = 3
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ? = 2
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ? = 2
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
 => ? = 3
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ? = 1
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ? = 3
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ? = 2
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
 => ? = 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
 => ? = 2
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ? = 4
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ? = 2
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ? = 1
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ? = 2
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
 => ? = 3
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
 => ? = 0
Description
The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Matching statistic: St000181
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000181: Posets ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 20%
Values
{{1}}
 => [1] => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 0 + 1
{{1,2}}
 => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 0 + 1
{{1},{2}}
 => [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 0 + 1
{{1,2,3}}
 => [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 0 + 1
{{1,2},{3}}
 => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 0 + 1
{{1,3},{2}}
 => [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 1
{{1},{2,3}}
 => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 1
{{1},{2},{3}}
 => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 1
{{1,2,3,4}}
 => [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 1
{{1,2,3},{4}}
 => [2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 0 + 1
{{1,2,4},{3}}
 => [2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 0 + 1
{{1,2},{3,4}}
 => [2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ? = 1 + 1
{{1,2},{3},{4}}
 => [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 1
{{1,3,4},{2}}
 => [3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 1 + 1
{{1,3},{2,4}}
 => [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ? = 0 + 1
{{1,3},{2},{4}}
 => [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 1
{{1,4},{2,3}}
 => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 0 + 1
{{1},{2,3,4}}
 => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 2 + 1
{{1},{2,3},{4}}
 => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 1 + 1
{{1,4},{2},{3}}
 => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 1
{{1},{2,4},{3}}
 => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 1 + 1
{{1},{2},{3,4}}
 => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 2 + 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 0 + 1
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ? = 3 + 1
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ? = 2 + 1
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ? = 2 + 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
 => ? = 3 + 1
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ? = 1 + 1
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ? = 3 + 1
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ? = 2 + 1
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
 => ? = 1 + 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
 => ? = 2 + 1
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ? = 4 + 1
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ? = 2 + 1
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ? = 1 + 1
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ? = 2 + 1
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
 => ? = 3 + 1
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
 => ? = 0 + 1
Description
The number of connected components of the Hasse diagram for the poset.
Matching statistic: St001890
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001890: Posets ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 20%
Values
{{1}}
 => [1] => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 0 + 1
{{1,2}}
 => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 0 + 1
{{1},{2}}
 => [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 0 + 1
{{1,2,3}}
 => [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 0 + 1
{{1,2},{3}}
 => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 0 + 1
{{1,3},{2}}
 => [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 1
{{1},{2,3}}
 => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 1
{{1},{2},{3}}
 => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 1
{{1,2,3,4}}
 => [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 1
{{1,2,3},{4}}
 => [2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 0 + 1
{{1,2,4},{3}}
 => [2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 0 + 1
{{1,2},{3,4}}
 => [2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ? = 1 + 1
{{1,2},{3},{4}}
 => [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 1
{{1,3,4},{2}}
 => [3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 1 + 1
{{1,3},{2,4}}
 => [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
 => ? = 0 + 1
{{1,3},{2},{4}}
 => [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 1
{{1,4},{2,3}}
 => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 0 + 1
{{1},{2,3,4}}
 => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ? = 2 + 1
{{1},{2,3},{4}}
 => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 1 + 1
{{1,4},{2},{3}}
 => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 1
{{1},{2,4},{3}}
 => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 1 + 1
{{1},{2},{3,4}}
 => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 2 + 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 0 + 1
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ? = 3 + 1
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ? = 2 + 1
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ? = 2 + 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
 => ? = 3 + 1
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ? = 1 + 1
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ? = 3 + 1
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ? = 2 + 1
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
 => ? = 1 + 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
 => ? = 2 + 1
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ? = 4 + 1
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ? = 2 + 1
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ? = 1 + 1
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ? = 2 + 1
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
 => ? = 3 + 1
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
 => ? = 0 + 1
Description
The maximum magnitude of the Möbius function of a poset. The '''Möbius function''' of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value $\mu(x, y)$ is equal to the signed sum of chains from $x$ to $y$, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.