Nonsymmetric Operads in Combinatorics

by Samuele Giraudo

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.

Product Details

ISBN-13:	9783030020736
Publisher:	Springer International Publishing
Publication date:	01/05/2019
Series:	SpringerBriefs in Computer Science
Edition description:	1st ed. 2018
Pages:	172
Product dimensions:	6.10(w) x 9.25(h) x (d)

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.

Table of Contents

Combinatorial Structures.- Trees and rewrite rules.- Combinatorial operands.- Main combinatorial operands.- Constructions, applications and generalizations.