The Symmetric Join Operad
  The join operad arises from the combinatorial study of the iterated join of simplices. We study a suitable simplicial version of this operad which includes the symmetries given by permutations of the factors of the join. From this combinatorics we construct an E-infinity operad which coacts naturally on the chains of a simplicial set. 
Michal Adamaszek, John D.S. Jones
math.AT math.CT