Set Operads in Combinatorics and Computer Science

Miguel A. Méndez (Autor)

Buch | Softcover

XV, 129 Seiten

2015
Springer International Publishing (Verlag)
978-3-319-11712-6 (ISBN)

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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.

Erscheint lt. Verlag	21.1.2015
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	XV, 129 p. 62 illus., 43 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	235 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Decomposition theory • Decomposition tree • Koszul operads • Modular decomposition • Set operads • Simple multiperson games
ISBN-10	3-319-11712-2 / 3319117122
ISBN-13	978-3-319-11712-6 / 9783319117126
Zustand	Neuware