A Semigroup Approach to Wreath-Product Extensions of Solomon's Descent Algebras
A Semigroup Approach to Wreath-Product Extensions of Solomon's Descent Algebras
There is a well-known combinatorial model, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this model to obtain a semigroup ${\cal F}_n^G$ associated with $G\wr S_n$, the wreath product of the symmetric group $S_n$ with an arbitrary group $G$. Techniques of Bidigare …