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 …

Solving the first nonmonotonic, longer-than-three instance of a classic enumeration problem,
we obtain the generating functionH (x) of all 1342-avoiding permutations of lengthnas well …

We give a bijection between Eulerian planar maps with prescribed vertex degrees, and
some plane trees that we call balanced Eulerian trees. To enumerate the latter, we introduce …

We review the various ways that stacks, their variations and their combinations, have been
used as sorting devices. In particular, we show that they have been a key motivator for the …

We prove a “decomposition lemma” that allows us to count preimages of certain sets of
permutations under West's stack-sorting map s. As a first application, we give a new proof of …

For each positive integer k, we consider five well-studied posets defined on the set of Dyck
paths of semilength k. We prove that uniquely sorted permutations avoiding various patterns …

In several cases, a sequence of free cumulants that counts certain binary plane trees
corresponds to a sequence of classical cumulants that counts the decreasing versions of the …

Involvement is a partial order on all finite permutations, of infinite dimension and having
subsets isomorphic to every countable partial order with finite descending chains. It has …

Bijections are obtained between nonseparable planar maps and two different kinds of trees:
description trees and skew ternary trees. A combinatorial relation between the latter and …

In his Ph. D. thesis, Julian West (Permutations with restricted subsequences and stack-
sortable permutations, MIT, 1990) studied in depth a map Π that acts on permutations of the …