George Grätzer started writing his General Lattice Theory in 1968. It was published in 1978.
It set out “to discuss in depth the basics of general lattice theory.” Almost 900 exercises, 193 …

We realize several combinatorial Hopf algebras based on set compositions, plane trees and
segmented compositions in terms of noncommutative polynomials in infinitely many …

Cambrian trees are oriented and labeled trees which fulfill local conditions around each
node generalizing the classical conditions for binary search trees. Similar to binary trees for …

We introduce permutrees, a unified model for permutations, binary trees, Cambrian trees
and binary sequences. On the combinatorial side, we study the rotation lattices on …

We generalize the “facial weak order” of a finite Coxeter group to a partial order on a set of
intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a …

This paper is motivated by the interplay between the Tamari lattice, J.-L. Loday's realization
of the associahedron, and J.-L. Loday and M. Ronco's Hopf algebra on binary trees. We …

We investigate the facial weak order, a poset structure that extends the weak order on a
finite Coxeter group $ W $ to the set of all faces of the permutahedron of $ W $. We first …

An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to
Hopf algebras that reflect the manner in which these objects compose and decompose …

We explore lattice structures on integer binary relations (ie binary relations on the set {1, 2,...,
n} for a fixed integer n) and on integer posets (ie partial orders on the set {1, 2,..., n} for a …

For an $ n $-tuple $ s $ of non-negative integers, the $ s $-weak order is a lattice structure
on $ s $-trees, generalizing the weak order on permutations. We first describe the join …