A sequence avoids a pattern π ∈ R if there is no subsequence that shares the same relative ordering as π. We develop techniques to understand how many queries it takes to test whether a sequence is π-avoiding or -far from π-avoiding. We initiate the study of searching in π-avoiding or nearly π-avoiding sequences, and show that it is possible to efficiently find most elements in a nearly (2, 1)-...

In this paper we study pattern avoidance for affine permutations. In particular, we show that for a given pattern p, there are only finitely many affine permutations in S̃n that avoid p if and only if p avoids the pattern 321. We then count the number of affine permutations that avoid a given pattern p for each p in S3, as well as give some conjectures for the patterns in S4.

We show that every avoidable pattern can be avoided by an infinite sequence of palindromes over a fixed finite alphabet. © 2009 Elsevier B.V. All rights reserved.

This tutorial presents an introduction to the studies undertaken by the authors and their collaborators between 1997 and 2009 on the topic of dissimilarity representations for pattern recognition.

Properties of shapes and shape patterns are investigated in order to represent shape pattern knowledge for supporting shape pattern recognition. It is based on the notion that shape patterns are classified in terms of similarity of spatial relationships as well as physical properties. Methods for shape pattern recognition are explained and examples from an implementation are presented.