Given an essential semilattice congruence $\equiv $ on the left weak order of a Coxeter
group $ W $, we define the Coxeter stack-sorting operator ${\bf S} _\equiv: W\to W $ by ${\bf …

We consider two orthogonal points of view on finite permutations, seen as pairs of linear
orders (corresponding to the usual one line representation of permutations as words) or …

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 …

In 1990, West initiated an extensive investigation of the stack-sorting map, a deterministic
version of Knuth's stack-sorting machine that acts on permutations. At first sight, this map …

We give three applications of a recently-proven" Decomposition Lemma," which allows one
to count preimages of certain sets of permutations under West's stack-sorting map s. We first …

We study permutations that are sorted by operators of the form S° α° S, where S is the usual
stack sorting operator introduced by Knuth and α is any D 8-symmetry obtained by …

We introduce an algorithm to determine when a sorting operation, such as stack-sort or
bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of …

We study preimages of permutations under the bubblesort operator $\mathbf {B} $. We
achieve a description of these preimages much more complete than what is known for the …

This thesis extends previous work of Claesson and Úlfarsson (2012) on algorithms for
computing the preimage of a pattern class under the stack-sort operator. We consider …

We present an algorithm, called BiSC, that describes the patterns avoided by a given set of
permutations. It automatically conjectures the statements of known theorems such as the …