Sorting Classes

Sorting Classes

Weak and strong sorting classes are pattern-closed classes that are also closed downwards under the weak and strong orders on permutations. They are studied using partial orders that capture both the subpermutation order and the weak or strong order. In both cases they can be characterised by forbidden permutations in the appropriate order. The connection with the corresponding forbidden permut...

Sorting classes – Extended Abstract

Weak and strong sorting classes are pattern-closed classes that are also closed downwards under the weak and strong orders on permutations. They are studied using partial orders that capture both the subpermutation order and the weak or strong order. In both cases they can be characterised by forbidden permutations in the appropriate order. The connection with the corresponding forbidden permut...

Sorting and preimages of pattern classes

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 West-2-stack-sortable permutations, that is permutations that are completely sorted when passed twice through a stack, in terms of patterns. We also solve the long-standing problem of describing West-3-stack-sortabl...

Permutation Classes, Sorting Algorithms, and Lattice Paths Tesi Di Dottorato Presentata Da Luca Ferrari

A Brief Look into Spike Sorting Methods

Spike sorting is a class of techniques used in the analysis of electrophysiological data. Studying the dynamics of neural activity via electrical recording relies on the ability to detect and sort neural spikes recorded from a number of neurons by the same electrode. This article reviews methods for detecting and classifying action potentials, a problem commonly referred to as spike sorting.