There are

(and possibly some waiting for verification)

**48 statistics**on**Integer compositions**in the database:(and possibly some waiting for verification)

St000008Integer compositions ⟶ ℤ

The major index of the composition.

St000047Integer compositions ⟶ ℤ

The number of standard immaculate tableaux of a given shape.

St000089Integer compositions ⟶ ℤ

The absolute variation of a composition.

St000090Integer compositions ⟶ ℤ

The variation of a composition.

St000091Integer compositions ⟶ ℤ

The descent variation of a composition.

St000277Integer compositions ⟶ ℤ

The number of ribbon shaped standard tableaux.

St000285Integer compositions ⟶ ℤ

The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions.

St000381Integer compositions ⟶ ℤ

The largest part of an integer composition.

St000382Integer compositions ⟶ ℤ

The first part of an integer composition.

St000383Integer compositions ⟶ ℤ

The last part of an integer composition.

St000657Integer compositions ⟶ ℤ

The smallest part of an integer composition.

St000757Integer compositions ⟶ ℤ

The length of the longest weakly inreasing subsequence of parts of an integer composition.

St000758Integer compositions ⟶ ℤ

The length of the longest staircase fitting into an integer composition.

St000760Integer compositions ⟶ ℤ

The length of the longest strictly decreasing subsequence of parts of an integer composition.

St000761Integer compositions ⟶ ℤ

The number of ascents in an integer composition.

St000762Integer compositions ⟶ ℤ

The sum of the positions of the weak records of an integer composition.

St000763Integer compositions ⟶ ℤ

The sum of the positions of the strong records of an integer composition.

St000764Integer compositions ⟶ ℤ

The number of strong records in an integer composition.

St000765Integer compositions ⟶ ℤ

The number of weak records in an integer composition.

St000766Integer compositions ⟶ ℤ

The number of inversions of an integer composition.

St000767Integer compositions ⟶ ℤ

The number of runs in an integer composition.

St000768Integer compositions ⟶ ℤ

The number of peaks in an integer composition.

St000769Integer compositions ⟶ ℤ

The major index of a composition regarded as a word.

St000805Integer compositions ⟶ ℤ

The number of peaks of the associated bargraph.

St000806Integer compositions ⟶ ℤ

The semiperimeter of the associated bargraph.

St000807Integer compositions ⟶ ℤ

The sum of the heights of the valleys of the associated bargraph.

St000808Integer compositions ⟶ ℤ

The number of up steps of the associated bargraph.

St000816Integer compositions ⟶ ℤ

The number of standard composition tableaux of the composition.

St000817Integer compositions ⟶ ℤ

The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions.

St000818Integer compositions ⟶ ℤ

The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions.

St000820Integer compositions ⟶ ℤ

The number of compositions obtained by rotating the composition.

St000899Integer compositions ⟶ ℤ

The maximal number of repetitions of an integer composition.

St000900Integer compositions ⟶ ℤ

The minimal number of repetitions of a part in an integer composition.

St000902Integer compositions ⟶ ℤ

The minimal number of repetitions of an integer composition.

St000903Integer compositions ⟶ ℤ

The number of different parts of an integer composition.

St000904Integer compositions ⟶ ℤ

The maximal number of repetitions of an integer composition.

St000905Integer compositions ⟶ ℤ

The number of different multiplicities of parts of an integer composition.

St001102Integer compositions ⟶ ℤ

The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132.

St001235Integer compositions ⟶ ℤ

The global dimension of the corresponding Comp-Nakayama algebra.

St001236Integer compositions ⟶ ℤ

The dominant dimension of the corresponding Comp-Nakayama algebra.

St001263Integer compositions ⟶ ℤ

The index of the maximal parabolic seaweed algebra associated with the composition.

St001312Integer compositions ⟶ ℤ

Number of parabolic noncrossing partitions indexed by the composition.

St001486Integer compositions ⟶ ℤ

The number of corners of the ribbon associated with an integer composition.

St001591Integer compositions ⟶ ℤ

The number of graphs with the given composition of multiplicities of Laplacian eigenvalues.

St001629Integer compositions ⟶ ℤ

The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.

St001673Integer compositions ⟶ ℤ

The degree of asymmetry of an integer composition.

St001675Integer compositions ⟶ ℤ

The number of parts equal to the part in the reversed composition.

St001777Integer compositions ⟶ ℤ

The number of weak descents in an integer composition.