Why such patterns? A few motivation points

Abstract

While getting familiar with results on patterns in later chapters, one not only has a chance to appreciate the beauty of combinatorics of patterns on words and permutations (which is interesting in its own right), but also to learn about connections of the field to other branches of combinatorics, mathematics, and theoretical computer science. The main application of patterns so far is that in many situations they provide a convenient language for describing various (combinatorial) objects. Such descriptions can be used in establishing properties (e.g., equidistribution results) of objects related to words or permutations restricted somehow by patterns (e.g., avoiding certain patterns). However, in most of the cases considered in the literature, the prime interest in linking pattern-restricted permutations/words to other objects is finding a bijection between the structures involved rather than also trying to find immediate applications.