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＜E-Book＞
Set Operads in Combinatorics and Computer Science / by Miguel A. Méndez
(SpringerBriefs in Mathematics. ISSN:21918201 ; 0)

Edition	1st ed. 2015.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2015
Language	English
Size	XV, 129 p. 62 illus., 43 illus. in color : online resource
Authors	*Méndez, Miguel A author SpringerLink (Online service)
Subjects	LCSH:Special functions LCSH:System theory LCSH:Operator theory FREE:Special Functions FREE:Complex Systems FREE:Operator Theory
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-11713-3

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