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 give bijections between bipolar-oriented (acyclic with unique source and sink) planar
maps and certain random walks, which show that the uniformly random bipolar-oriented …

In 1990, Schnyder used a 3-spanning-tree decomposition of a simple triangulation, now
known as the Schnyder wood, to give a fundamental grid-embedding algorithm for planar …

We introduce a general technique for proving estimates for certain random planar maps
which belong to the γ γ-Liouville quantum gravity (LQG) universality class for γ ∈ (0, 2) …

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 …

A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint
rectangles, such that no four rectangles meet in a point. In this work we present a versatile …

This article presents a unified bijective scheme between planar maps and blossoming trees,
where a blossoming tree is defined as a spanning tree of the map decorated with some …

In this paper, we enumerate two families of pattern-avoiding permutations: those avoiding
the vincular pattern 2413, which we call semi-Baxter permutations, and those avoiding the …

In the first part of this survey, we consider planar graphs that can be represented by a
dissections of a rectangle into rectangles. In rectangular drawings, the corners of the …

We define and study a combinatorial Hopf algebra dRec with basis elements indexed by
diagonal rectangulations of a square. This Hopf algebra provides an intrinsic combinatorial …