We give a survey of the Lagrange inversion formula, including different versions and proofs,
with applications to combinatorial and formal power series identities.

The m-Tamari lattice of F. Bergeron is an analogue of the classical Tamari order defined on
objects counted by Fuss-Catalan numbers, such as m-Dyck paths or (m+ 1)-ary trees. On …

We propose several constructions of commutative or cocommutative Hopf algebras based
on various combinatorial structures and investigate the relations between them. A …

Combining the definition of 0-Hecke monoids with that of Kiselman semigroups, we define
what we call Kiselman quotients of 0-Hecke monoids associated with simply laced Dynkin …

We introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases
labeled by colored permutations. When the color set is a semigroup, an internal product can …

Bell polynomials appear in several combinatorial constructions throughout mathematics.
Perhaps most naturally in the combinatorics of set partitions, but also when studying …

One of the main virtues of trees is the representation of formal solutions of various functional
equations which can be cast in the form of fixed point problems. Basic examples include …

The functional equation defining the free cumulants in free probability is lifted successively
to the noncommutative Faà di Bruno algebra, and then to the group of a free operad over …

Associated with any Coxeter group is a Coxeter monoid, which has the same elements, and
the same identity, but a different multiplication.(Some authors call these Coxeter monoids 0 …

In this paper, we define and study what we call the double Catalan monoid. This monoid is
the image of a natural map from the 0-Hecke monoid to the monoid of binary relations. We …