Nonsymmetric Operads in Combinatorics (eBook)

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.

- Chapter 1. Combinatorial Structures 1. Combinatorial sets and combinatorial objects 1.1 Combinatorial sets 1.2 Operations over combinatorial sets 1.3 Main combinatorial sets 2. Combinatorial spaces 2.1 Polynomials on combinatorial sets 2.2 Operations over combinatorial spaces 2.3 Combinatorial bialgebras 2.4 Types of combinatorial bialgebras- Chapter 2. Trees and rewrite rules 1. Syntax trees 1.1 planar rooted trees 1.2 Families of planar rooted trees 1.3 syntax trees 2 Rewrite rules 2.1 Combinatorial posets 2.2 Rewrite rules on combinatorial sets 2.3 Rewrite ruls on combinatorial spaces 2.4 Syntax tree patterns and rewrite rules- Chapter 3 Combinatorial operands 1. Nonsymmetric operands 2 Free operands 3 Presentation by generators and relations 4 Algebras over operands 5 Koszul operands and Koszul duality- Chapter 4 Main combinatorial operands 1. Associative and magmatic operands 2 Operands and permutations 3 Dendriform operand 4 operands of rational fractions- Chapter 5 Constructions, applications and generalizations 1. Series on operands 2 Functors to operands 3 Functors from operands 4 Beyond operands