Louis Solomon showed that the group algebra of the symmetric group
$$\mathfrak{S}_{n}$$ n has a subalgebra called the descent algebra, generated by
sums of permutations with a given descent set. In fact, he showed that every
Coxeter group has something that can be called a descent algebra. There is also
a commutative, semisimple subalgebra of Solomon's descent algebra generated by
sums of permutat... hiện toàn bộ