Overview
- Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form more complex ones. Coming historically from algebraic topology, operads intervene now as important objects in computer science and in combinatorics. A lot of operads involving combinatorial objects highlight some of their properties and allow to discover new ones.
- This book portrays the main elements of this theory under a combinatorial point of view and exposes the links it maintains with computer science and combinatorics. Examples of operads appearing in combinatorics are studied. The modern treatment of operads consisting in considering the space of formal power series associated with an operad is developed. Enrichments of nonsymmetric operads as colored, cyclic, and symmetric operads are reviewed.
- This text is addressed to any computer scientist or combinatorist who looks a complete and a modern description of the theory of nonsymmetric operads. Evenly, this book is intended to an audience of algebraists who are looking for an original point of view fitting in the context of combinatorics.
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About this book
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form more complex ones. Coming historically from algebraic topology, operads intervene now as important objects in computer science and in combinatorics. A lot of operads involving combinatorial objects highlight some of their properties and allow to discover new ones.
This book portrays the main elements of this theory under a combinatorial point of view and exposes the links it maintains with computer science and combinatorics. Examples of operads appearing in combinatorics are studied. The modern treatment of operads consisting in considering the space of formal power series associated with an operad is developed. Enrichments of nonsymmetric operads as colored, cyclic, and symmetric operads are reviewed.
This book portrays the main elements of this theory under a combinatorial point of view and exposes the links it maintains with computer science and combinatorics. Examples of operads appearing in combinatorics are studied. The modern treatment of operads consisting in considering the space of formal power series associated with an operad is developed. Enrichments of nonsymmetric operads as colored, cyclic, and symmetric operads are reviewed.
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Table of contents (6 chapters)
Authors and Affiliations
About the author
Samuele Giraudo is an associate professor at LIGM, University of Paris-Est Marne-la-Vallée in France. He received a PhD and then an accreditation to supervise research, both in computer science. His research interests are primarily in combinatorics and algebraic combinatorics. His research works focus on Hopf bialgeras, operads, and applications of methods coming from algebra to solve enumerative problems.
Bibliographic Information
Book Title: Nonsymmetric Operads in Combinatorics
Authors: Samuele Giraudo
DOI: https://doi.org/10.1007/978-3-030-02074-3
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-030-02073-6Published: 18 January 2019
eBook ISBN: 978-3-030-02074-3Published: 04 January 2019
Edition Number: 1
Number of Pages: IX, 172
Number of Illustrations: 4 b/w illustrations, 157 illustrations in colour
Topics: Mathematical Logic and Formal Languages, Math Applications in Computer Science, Discrete Mathematics in Computer Science