Descent algebra

In algebra, Solomon's descent algebra of a Coxeter group is a subalgebra of the integral group ring of the Coxeter group, introduced by.

The descent algebra of the symmetric group

In the special case of the symmetric group S_n, the descent algebra is given by the elements of the group ring such that permutations with the same descent set have the same coefficients. > σ The descent algebra of the symmetric group S_n has dimension 2^n-1. It contains the peak algebra as a left ideal.