ENGLISH

Nonsymmetric Operads in Combinatorics

By Samuele Giraudo

Book information

Publisher
Springer International Publishing
Year
2018
ISBN
978-3-030-02073-6, 978-3-030-02074-3
Language
english
Format
PDF
Filesize
5 MB (4986046 bytes)
Edition
1st ed.
Pages
IX, 172\176
Time added
2019-04-19 19:00:00
Computer Science; Mathematical Logic and Formal La

Description

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. Front Matter ....Pages i-ix Introduction (Samuele Giraudo)....Pages 1-8 Enriched Collections (Samuele Giraudo)....Pages 9-34 Treelike Structures (Samuele Giraudo)....Pages 35-57 Algebraic Structures (Samuele Giraudo)....Pages 59-93 Nonsymmetric Operads (Samuele Giraudo)....Pages 95-135 Applications and Generalizations (Samuele Giraudo)....Pages 137-165 Back Matter ....Pages 167-172

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