Identifier
There are 101 statistics on Set partitions in the database. There are possibly some more waiting for verification.

St000105Set partitions ⟶ ℤ
The number of blocks in the set partition.
St000163Set partitions ⟶ ℤ
The size of the orbit of the set partition under rotation.
St000211Set partitions ⟶ ℤ
The rank of the set partition.
St000229Set partitions ⟶ ℤ
Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition.
St000230Set partitions ⟶ ℤ
Sum of the minimal elements of the blocks of a set partition.
St000231Set partitions ⟶ ℤ
Sum of the maximal elements of the blocks of a set partition.
St000232Set partitions ⟶ ℤ
The number of crossings of a set partition.
St000233Set partitions ⟶ ℤ
The number of nestings of a set partition.
St000247Set partitions ⟶ ℤ
The number of singleton blocks of a set partition.
St000248Set partitions ⟶ ℤ
The number of anti-singletons of a set partition.
St000249Set partitions ⟶ ℤ
The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition.
St000250Set partitions ⟶ ℤ
The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition.
St000251Set partitions ⟶ ℤ
The number of nonsingleton blocks of a set partition.
St000253Set partitions ⟶ ℤ
The crossing number of a set partition.
St000254Set partitions ⟶ ℤ
The nesting number of a set partition.
St000490Set partitions ⟶ ℤ
The intertwining number of a set partition.
St000491Set partitions ⟶ ℤ
The number of inversions of a set partition.
St000492Set partitions ⟶ ℤ
The rob statistic of a set partition.
St000493Set partitions ⟶ ℤ
The los statistic of a set partition.
St000496Set partitions ⟶ ℤ
The rcs statistic of a set partition.
St000497Set partitions ⟶ ℤ
The lcb statistic of a set partition.
St000498Set partitions ⟶ ℤ
The lcs statistic of a set partition.
St000499Set partitions ⟶ ℤ
The rcb statistic of a set partition.
St000502Set partitions ⟶ ℤ
The number of successions of a set partitions.
St000503Set partitions ⟶ ℤ
The maximal difference between two elements in a common block.
St000504Set partitions ⟶ ℤ
The cardinality of the first block of a set partition.
St000505Set partitions ⟶ ℤ
The biggest entry in the block containing the 1.
St000554Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,2},{3}} in a set partition.
St000555Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} in a set partition.
St000556Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} in a set partition.
St000557Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} in a set partition.
St000558Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,2}} in a set partition.
St000559Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2,4}} in a set partition.
St000560Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,2},{3,4}} in a set partition.
St000561Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,2,3}} in a set partition.
St000562Set partitions ⟶ ℤ
The number of internal points of a set partition.
St000563Set partitions ⟶ ℤ
The number of overlapping pairs of blocks of a set partition.
St000564Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2}} in a set partition.
St000565Set partitions ⟶ ℤ
The major index of a set partition.
St000572Set partitions ⟶ ℤ
The dimension exponent of a set partition.
St000573Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton and 2 a maximal element.
St000574Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2}} such that 1 is a minimal and 2 a maximal element.
St000575Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element and 2 a singleton.
St000576Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal and 2 a minimal element.
St000577Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element.
St000578Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton.
St000579Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2}} such that 2 is a maximal element.
St000580Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 2 is minimal, 3 is maximal.
St000581Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal.
St000582Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 3 is maximal, (1,3) are consecutive in a block.
St000583Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1, 2 are maximal.
St000584Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal, 3 is maximal.
St000585Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block.
St000586Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal.
St000587Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal.
St000588Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are minimal, 2 is maximal.
St000589Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block.
St000590Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 1 is maximal, (2,3) are consecutive in a block.
St000591Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 2 is maximal.
St000592Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 1 is maximal.
St000593Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 1,2 are minimal.
St000594Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block.
St000595Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal.
St000596Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1 is maximal.
St000597Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, (2,3) are consecutive in a block.
St000598Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, 3 is maximal, (2,3) are consecutive in a block.
St000599Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that (2,3) are consecutive in a block.
St000600Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block.
St000601Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, (2,3) are consecutive in a block.
St000602Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal.
St000603Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 2,3 are minimal.
St000604Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 2 is maximal.
St000605Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 3 is maximal, (2,3) are consecutive in a block.
St000606Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1,3 are maximal, (2,3) are consecutive in a block.
St000607Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 3 is maximal, (2,3) are consecutive in a block.
St000608Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 1,2 are minimal, 3 is maximal.
St000609Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal.
St000610Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal.
St000611Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal.
St000612Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, (2,3) are consecutive in a block.
St000613Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block.
St000614Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, 3 is maximal, (2,3) are consecutive in a block.
St000615Set partitions ⟶ ℤ
The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are maximal.
St000695Set partitions ⟶ ℤ
The number of blocks in the first part of the atomic decomposition of a set partition.
St000728Set partitions ⟶ ℤ
The dimension of a set partition.
St000729Set partitions ⟶ ℤ
The minimal arc length of a set partition.
St000730Set partitions ⟶ ℤ
The maximal arc length of a set partition.
St000747Set partitions ⟶ ℤ
A variant of the major index of a set partition.
St000748Set partitions ⟶ ℤ
The major index of the permutation obtained by flattening the set partition.
St000793Set partitions ⟶ ℤ
The length of the longest partition in the vacillating tableau corresponding to a set partition.
St000823Set partitions ⟶ ℤ
The number of unsplittable factors of the set partition.
St000839Set partitions ⟶ ℤ
The largest opener of a set partition.
St000925Set partitions ⟶ ℤ
The number of topologically connected components of a set partition.
St000971Set partitions ⟶ ℤ
The smallest closer of a set partition.
St001050Set partitions ⟶ ℤ
The number of terminal closers of a set partition.
St001051Set partitions ⟶ ℤ
The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition.
St001062Set partitions ⟶ ℤ
The maximal size of a block of a set partition.
St001075Set partitions ⟶ ℤ
The minimal size of a block of a set partition.
St001094Set partitions ⟶ ℤ
The depth index of a set partition.
St001151Set partitions ⟶ ℤ
The number of blocks with odd minimum.
St001153Set partitions ⟶ ℤ
The number of blocks with even minimum in a set partition.