There are

(and possibly some waiting for verification)

**71 statistics**on**Binary words**in the database:(and possibly some waiting for verification)

St000288Binary words ⟶ ℤ

The number of ones in a binary word.

St000289Binary words ⟶ ℤ

The decimal representation of a binary word.

St000290Binary words ⟶ ℤ

The major index of a binary word.

St000291Binary words ⟶ ℤ

The number of descents of a binary word.

St000292Binary words ⟶ ℤ

The number of ascents of a binary word.

St000293Binary words ⟶ ℤ

The number of inversions of a binary word.

St000294Binary words ⟶ ℤ

The number of distinct factors of a binary word.

St000295Binary words ⟶ ℤ

The length of the border of a binary word.

St000296Binary words ⟶ ℤ

The length of the symmetric border of a binary word.

St000297Binary words ⟶ ℤ

The number of leading ones in a binary word.

St000326Binary words ⟶ ℤ

The position of the first one in a binary word after appending a 1 at the end.

St000347Binary words ⟶ ℤ

The inversion sum of a binary word.

St000348Binary words ⟶ ℤ

The non-inversion sum of a binary word.

St000389Binary words ⟶ ℤ

The number of runs of ones of odd length in a binary word.

St000390Binary words ⟶ ℤ

The number of runs of ones in a binary word.

St000391Binary words ⟶ ℤ

The sum of the positions of the ones in a binary word.

St000392Binary words ⟶ ℤ

The length of the longest run of ones in a binary word.

St000393Binary words ⟶ ℤ

The number of strictly increasing runs in a binary word.

St000518Binary words ⟶ ℤ

The number of distinct subsequences in a binary word.

St000519Binary words ⟶ ℤ

The largest length of a factor maximising the subword complexity.

St000529Binary words ⟶ ℤ

The number of permutations whose descent word is the given binary word.

St000543Binary words ⟶ ℤ

The size of the conjugacy class of a binary word.

St000626Binary words ⟶ ℤ

The minimal period of a binary word.

St000627Binary words ⟶ ℤ

The exponent of a binary word.

St000628Binary words ⟶ ℤ

The balance of a binary word.

St000629Binary words ⟶ ℤ

The defect of a binary word.

St000630Binary words ⟶ ℤ

The length of the shortest palindromic decomposition of a binary word.

St000631Binary words ⟶ ℤ

The number of distinct palindromic decompositions of a binary word.

St000682Binary words ⟶ ℤ

The Grundy value of Welter's game on a binary word.

St000691Binary words ⟶ ℤ

The number of changes of a binary word.

St000753Binary words ⟶ ℤ

The Grundy value for the game of Kayles on a binary word.

St000792Binary words ⟶ ℤ

The Grundy value for the game of ruler on a binary word.

St000826Binary words ⟶ ℤ

The stopping time of the decimal representation of the binary word for the 3x+1 problem.

St000827Binary words ⟶ ℤ

The decimal representation of a binary word with a leading 1.

St000847Binary words ⟶ ℤ

The number of standard Young tableaux whose descent set is the binary word.

St000875Binary words ⟶ ℤ

The semilength of the longest Dyck word in the Catalan factorisation of a binary word.

St000876Binary words ⟶ ℤ

The number of factors in the Catalan decomposition of a binary word.

St000877Binary words ⟶ ℤ

The depth of the binary word interpreted as a path.

St000878Binary words ⟶ ℤ

The number of ones minus the number of zeros of a binary word.

St000885Binary words ⟶ ℤ

The number of critical steps in the Catalan decomposition of a binary word.

St000921Binary words ⟶ ℤ

The number of internal inversions of a binary word.

St000922Binary words ⟶ ℤ

The minimal number such that all substrings of this length are unique.

St000982Binary words ⟶ ℤ

The length of the longest constant subword.

St000983Binary words ⟶ ℤ

The length of the longest alternating subword.

St001267Binary words ⟶ ℤ

The length of the Lyndon factorization of the binary word.

St001313Binary words ⟶ ℤ

The number of Dyck paths above the lattice path given by a binary word.

St001355Binary words ⟶ ℤ

Number of non-empty prefixes of a binary word that contain equally many 0's and 1's.

St001365Binary words ⟶ ℤ

The number of lattice paths of the same length weakly above the path given by a binary word.

St001371Binary words ⟶ ℤ

The length of the longest Yamanouchi prefix of a binary word.

St001372Binary words ⟶ ℤ

The length of a longest cyclic run of ones of a binary word.

St001413Binary words ⟶ ℤ

Half the length of the longest even length palindromic prefix of a binary word.

St001414Binary words ⟶ ℤ

Half the length of the longest odd length palindromic prefix of a binary word.

St001415Binary words ⟶ ℤ

The length of the longest palindromic prefix of a binary word.

St001416Binary words ⟶ ℤ

The length of a longest palindromic factor of a binary word.

St001417Binary words ⟶ ℤ

The length of a longest palindromic subword of a binary word.

St001419Binary words ⟶ ℤ

The length of the longest palindromic factor beginning with a one of a binary word.

St001420Binary words ⟶ ℤ

Half the length of a longest factor which is its own reverse-complement of a binary word.

St001421Binary words ⟶ ℤ

Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word.

St001423Binary words ⟶ ℤ

The number of distinct cubes in a binary word.

St001424Binary words ⟶ ℤ

The number of distinct squares in a binary word.

St001436Binary words ⟶ ℤ

The index of a given binary word in the lex-order among all its cyclic shifts.

St001437Binary words ⟶ ℤ

The flex of a binary word.

St001485Binary words ⟶ ℤ

The modular major index of a binary word.

St001491Binary words ⟶ ℤ

The number of indecomposable projective-injective modules in the algebra corresponding to a subset.

St001524Binary words ⟶ ℤ

The degree of symmetry of a binary word.

St001721Binary words ⟶ ℤ

The degree of a binary word.

St001722Binary words ⟶ ℤ

The number of minimal chains with small intervals between a binary word and the top element.

St001730Binary words ⟶ ℤ

The number of times the path corresponding to a binary word crosses the base line.

St001838Binary words ⟶ ℤ

The number of nonempty primitive factors of a binary word.

St001884Binary words ⟶ ℤ

The number of borders of a binary word.

St001885Binary words ⟶ ℤ

The number of binary words with the same proper border set.