Set Operads in Combinatorics and Computer Science [Paperback]

This monograph has two main objectives. The first one is to give a self-contained?exposition of the relevant facts about set operads, in the context?of combinatorial species and its operations. This approach has various advantages:?one of them is that the definition of combinatorial operations on?species, product, sum, substitution and derivative, are simple and natural.?They were designed as the set theoretical counterparts of the homonym operations?on exponential generating functions, giving an immediate insight on the?combinatorial meaning of them. The second objective is more ambitious. Before formulating it, authors?present?a brief historic account on the sources of decomposition theory. For more than?forty years decompositions of discrete structures have been studied in different?branches of discrete mathematics: combinatorial optimization, network?and graph theory, switching design or boolean functions, simple multi-person?games and clutters, etc.

Introduction.- Preliminaries on Species and Set Operads.- Operations on Species and Set Operads.- Decomposition Theory.- Rigid Operads.- Posets from Cancellative Operads and Koszul Duality.- Appendix.

Gives a detailed?elementary introduction to set operads from the point of view of species, the advantages of this approach?are explained in the abstract

Settles decomposition theory in to the area of domain of a very general and powerful machinery: set operads and operads in general

Would be of the interest to computer scientists?as well as to the operadic community

US