Any permutation of ordered n-element set [n]=:{1,..., n} may be regarded as introducing a
(possibly null) measure of disorder to that set. For example, the natural order of [7] is …

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 …

Given two permutations σ and π, the Permutation Pattern problem asks if σ is a subpattern of
π. We show that the problem can be solved in time 2 O (ℓ 2 log ℓ). n, where ℓ=| σ| and n=| π …

We initiate the study of limit shapes for random permutations avoiding a given pattern.
Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of …

In this work we present a general and versatile algorithmic framework for exhaustively
generating a large variety of different combinatorial objects, based on encoding them as …

In this work we present a general and versatile algorithmic framework for exhaustively
generating a large variety of different combinatorial objects, based on encoding them as …

We set up a new notion of local convergence for permutations and we prove a
characterization in terms of proportions of consecutive pattern occurrences. We also …

Using an unprecedented technique involving diagonals of non-rational generating functions,
we prove that among the permutations of length $ n $ with $ i $ fixed points and $ j …

In this paper, we construct a bijection between 3142-avoiding permutations and 3241-
avoiding permutations which proves the equidistribution of five classical set-valued statistics …

We consider the involutions known as" toggles," which have been used to give simplified
proofs of the fundamental properties of the promotion and evacuation maps. We transfer …