This paper stands at the interface between combinatorial Hopf algebra theory and
renormalization theory. Its plan is as follows: Sec. 1.1 is the introduction, and contains an …

Publisher Summary This chapter focuses on the Hopf algebras in renormalization. The
chapter presents the Birkhoff decomposition. This chapter also explains the BCH approach …

This research monograph is divided into three parts. Broadly speaking, Part I belongs to the
realm of category theory, while Parts II and III pertain to algebraic combinatorics, although …

These notes--originating from a one-semester class by their second author at the University
of Minnesota--survey some of the most important Hopf algebras appearing in combinatorics …

We introduce a monoid structure on the set of binary search trees, by a process very similar
to the construction of the plactic monoid, the Robinson–Schensted insertion being replaced …

Generalized permutahedra are a family of polytopes with a rich combinatorial structure and
strong connections to optimization. We prove that they are the universal family of polyhedra …

We introduce a new basis for quasisymmetric functions, which arise from a specialization of
nonsymmetric Macdonald polynomials to standard bases, also known as Demazure atoms …

For positive integers $ i_1,..., i_k $ with $ i_1> 1$, we define the multiple $ t $-value $ t
(i_1,..., i_k) $ as the sum of those terms in the usual infinite series for the multiple zeta value …

The goal of this paper is to show that valuation theory and Hopf theory are compatible on the
class of generalized permutahedra. We prove that the Hopf structure on these polyhedra …

An extended version of a series of lectures given at Bogota in december 2002. It consists in
a presentation of some aspects of Connes' and Kreimer's work on renormalization in the …