| Abstract: | The peak set of a permutation  is the set {i : (i – 1) < (i) > (i + 1)}. The group algebra of the symmetric group S
n admits a subalgebra in which elements are sums of permutations with a common descent set. In this paper we show the existence of a subalgebra of this descent algebra in which elements are sums of permutations sharing a common peak set. To prove the existence of this peak algebra we use the theory of enriched (P,  )-partitions and the algebra of quasisymmetric peak functions studied by Stembridge (Trans. Amer. Math. Soc. 349 (1997) 763–788). |
