Free quasi-symmetric functions, product actions and quantum field theory   of partitions
  We examine two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender's QFT of partitions. We end by exploring possibilities to construct noncommutative analogues. 
Gerard Henry Edmond Duchamp (LIPN), Jean-Gabriel Luque (IGM), Karol A.   Penson (LPTL), Christophe Tollu (LIPN)