There has been considerable interest recently in the subject of patterns in permutations and
words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and …

Hints of the study of patterns in permutations date back a century, to Volume I, Section III,
Chapter V of MacMahon's 1915 magnum opus Combinatory Analysis [126]. In that work …

A geometric grid class consists of those permutations that can be drawn on a specified set of
line segments of slope $\pm 1$ arranged in a rectangular pattern governed by a matrix …

Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically
and rigorously study the structure of combinatorial objects and derive their counting …

We introduce and characterise grid classes, which are natural generalisations of other well-
studied permutation classes. This characterisation allows us to give a new, short proof of the …

We establish a phase transition for permutation classes (downsets of permutations under the
permutation containment order): there is an algebraic number κ, approximately 2.20557, for …

While the theory of labelled well-quasi-order has received significant attention in the graph
setting, it has not yet been considered in the context of permutation patterns. We initiate this …

The study of pattern classes is the study of the involvement order on finite permutations. This
order can be traced back to the work of Knuth. In recent years the area has attracted the …

We uncover a connection between two seemingly unrelated notions: lettericity, from
structural graph theory, and geometric griddability, from the world of permutation patterns …

We describe a new method for finding patterns in permutations that produce a given pattern
after the permutation has been passed once through a stack. We use this method to …