There are

(and possibly some waiting for verification)

**68 statistics**on**Finite Cartan types**in the database:(and possibly some waiting for verification)

St000106Finite Cartan types ⟶ ℤ

The size of the associated Weyl group.

St000107Finite Cartan types ⟶ ℤ

The dimension of the representation $V(\Lambda_1)$.

St000113Finite Cartan types ⟶ ℤ

The rank of the Cartan type.

St000138Finite Cartan types ⟶ ℤ

The Catalan number of an irreducible finite Cartan type.

St000139Finite Cartan types ⟶ ℤ

The Coxeter number of a finite Cartan type.

St000140Finite Cartan types ⟶ ℤ

The positive Catalan number of an irreducible finite Cartan type.

St000821Finite Cartan types ⟶ ℤ

The determinant of the Cartan matrix.

St000851Finite Cartan types ⟶ ℤ

The third Fuss-Catalan number of a finite Cartan type.

St000852Finite Cartan types ⟶ ℤ

The second Fuss-Catalan number of a finite Cartan type.

St000853Finite Cartan types ⟶ ℤ

The number of almost positive roots of a finite Cartan type.

St000854Finite Cartan types ⟶ ℤ

The number of orbits of reflections of a finite Cartan type.

St000855Finite Cartan types ⟶ ℤ

The number of full-support reflections in the Weyl group of a finite Cartan type.

St000856Finite Cartan types ⟶ ℤ

The number of conjugacy classes in the Weyl group of a finite Cartan type.

St000857Finite Cartan types ⟶ ℤ

The number of reflections of the Weyl group of a finite Cartan type.

St000858Finite Cartan types ⟶ ℤ

The number of factorizations of any Coxeter element into reflections of a finite Cartan type.

St000859Finite Cartan types ⟶ ℤ

The number of parking functions of a finite Cartan type.

St000860Finite Cartan types ⟶ ℤ

The size of the center of the Weyl group of a finite Cartan type.

St000861Finite Cartan types ⟶ ℤ

The maximal dimension of an irreducible representation of the Weyl group of a finite Cartan type.

St000865Finite Cartan types ⟶ ℤ

The number of Coxeter elements in the Weyl group of a finite Cartan type.

St000960Finite Cartan types ⟶ ℤ

The permanent of the Cartan matrix of a finite Cartan type.

St001053Finite Cartan types ⟶ ℤ

The second positive Fuss-Catalan number of a finite Cartan type.

St001054Finite Cartan types ⟶ ℤ

The third positive Fuss-Catalan number of a finite Cartan type.

St001143Finite Cartan types ⟶ ℤ

The number of pairs in the Weyl group of given type with mu-coefficient of the Kazhdan Lusztig polynomial being non-zero.

St001144Finite Cartan types ⟶ ℤ

The largest mu-coefficient of the Kazhdan Lusztig polynomial occurring in the Weyl group of given type.

St001145Finite Cartan types ⟶ ℤ

The largest coefficient in a Kazhdan Lusztig polynomial of the Weyl group of given type.

St001146Finite Cartan types ⟶ ℤ

The number of Grassmannian elements in the Coxeter group of the given type.

St001147Finite Cartan types ⟶ ℤ

The number of minuscule dominant weights in the weight lattice of a finite Cartan type.

St001148Finite Cartan types ⟶ ℤ

The dimension of the adjoint representation of the Lie group of given type.

St001149Finite Cartan types ⟶ ℤ

The dimension of the quasi-minuscule representation of the Lie group of given type.

St001150Finite Cartan types ⟶ ℤ

The minimal dimension of a faithful linear representation of the Lie algebra of given type.

St001154Finite Cartan types ⟶ ℤ

The dual Coxeter number of a finite Cartan type.

St001155Finite Cartan types ⟶ ℤ

The number of conjugacy classes of subgroups of the Weyl group of given type.

St001156Finite Cartan types ⟶ ℤ

The Dynkin index of the Lie algebra of given type.

St001157Finite Cartan types ⟶ ℤ

The exponent of the Weyl group of given type.

St001158Finite Cartan types ⟶ ℤ

The size of the mutation class of quivers of given type.

St001173Finite Cartan types ⟶ ℤ

The number of commutative positive roots in the root system of the given finite Cartan type.

St001369Finite Cartan types ⟶ ℤ

The largest coefficient in the highest root in the root system of a Cartan type.

St001370Finite Cartan types ⟶ ℤ

The degree of the largest fundamental representation associated with a Cartan type.

St001443Finite Cartan types ⟶ ℤ

The largest coefficient in the PoincarĂ© polynomial of the Weyl group of given Cartan type.

St001467Finite Cartan types ⟶ ℤ

The number of involutions in the Weyl group of a given Cartan type.

St001495Finite Cartan types ⟶ ℤ

The maximal order of an element in the Weyl group of a given Cartan type.

St001585Finite Cartan types ⟶ ℤ

The number of reduced decompositions of the longest element of the Weyl group of the given Cartan type.

St001653Finite Cartan types ⟶ ℤ

The number of fully commutative elements of the Weyl group of the given Cartan type.

St001676Finite Cartan types ⟶ ℤ

The gamma number of the Weyl group of a Cartan type.

St001678Finite Cartan types ⟶ ℤ

The symmetric bilinear form applied to the highest root and the Weyl vector of a finite Cartan type.

St001680Finite Cartan types ⟶ ℤ

The sum of the squares of the exponents of the Weyl group of the finite Cartan type.

St001700Finite Cartan types ⟶ ℤ

The maximum degree of the Hasse diagram of the strong Bruhat order in the Weyl group of the Cartan type.

St001701Finite Cartan types ⟶ ℤ

The maximum down-degree of the Hasse diagram of the strong Bruhat order in the Weyl group of the Cartan type.

St001747Finite Cartan types ⟶ ℤ

The number of zeros in the character table of the Weyl group of a Cartan type.

St001748Finite Cartan types ⟶ ℤ

The number of negative entries in the character table of the Weyl group of a Cartan type.

St001749Finite Cartan types ⟶ ℤ

The number of distinct dimensions of the irreducible representations of the Weyl group of a finite Cartan type.

St001750Finite Cartan types ⟶ ℤ

The number of even entries in the character table of the Weyl group of a Cartan type.

St001751Finite Cartan types ⟶ ℤ

The number of proper elements in the Weyl group of a finite Cartan type.

St001752Finite Cartan types ⟶ ℤ

The number of elements of maximal order in the Weyl group of a finite Cartan type.

St001753Finite Cartan types ⟶ ℤ

The number of subsets of the positive roots that form a basis of the associated vector space.

St001755Finite Cartan types ⟶ ℤ

The number of pairwise different full-rank reflection subgroups of the associated Weyl group.

St001756Finite Cartan types ⟶ ℤ

The number of minimal subsets of reflections that generate the group.

St001787Finite Cartan types ⟶ ℤ

The number of subgroups of the Weyl group of given type.

St001788Finite Cartan types ⟶ ℤ

The number of types of parabolic subgroups of the associated Weyl group.

St001789Finite Cartan types ⟶ ℤ

The number of types of reflection subgroups of the associated Weyl group.

St001790Finite Cartan types ⟶ ℤ

The number of reflection subgroups of the associated Weyl group.

St001791Finite Cartan types ⟶ ℤ

The number of parabolic subgroups of the associated Weyl group.

St001849Finite Cartan types ⟶ ℤ

The atomic length of the longest element.

St001886Finite Cartan types ⟶ ℤ

The number of orbits of the rowmotion operator on the root poset of a finite Cartan type.

St001887Finite Cartan types ⟶ ℤ

The order of rowmotion on the root poset of a finite Cartan type.

St001888Finite Cartan types ⟶ ℤ

The number of connected elements in the Coxeter group corresponding to a finite Cartan type.

St001891Finite Cartan types ⟶ ℤ

The size of a smallest Eulerian poset which does not appear as an interval in the Bruhat order of the Weyl group.

St001897Finite Cartan types ⟶ ℤ

The minimal degree of a faithful permutation representation of a Weyl group.