Set Operads in Combinatorics and Computer Science

This monograph has two main objectives. The first one is to give a self-containedexposition of the relevant facts about set operads, in the contextof combinatorial species and its operations. This approach has various advantages:one of them is that the definition of combinatorial operations onspecies, product, sum, substitution and derivative, are simple and natural.They were designed as the set theoretical counterparts of the homonym operationson exponential generating functions, giving an immediate insight on thecombinatorial meaning of them. The second objective is more ambitious. Before formulating it, authorspresenta brief historic account on the sources of decomposition theory. For more thanforty years decompositions of discrete structures have been studied in differentbranches of discrete mathematics: combinatorial optimization, networkand graph theory, switching design or boolean functions, simple multi-persongames and clutters, etc.