Set Operads in Combinatorics and Computer Science

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.

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 Includes supplementary material: sn.pub/extras

Inhalt

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.