There are 49 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.
St001931Integer compositions ⟶ ℤ
The weak major index of an integer composition regarded as a word.