**Identifier**

**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.