ABSTRACT
A statistic (see Definition 1.17) on a set partition is a characteristic such as the number of blocks, rises, levels, descents, odd letters, etc. In this chapter we will focus on “word-statistics”, a special type of statistics. A word-statistic is a statistic that can be expressed in terms of occurrences of subword patterns. The current chapter will present several results and techniques to obtain generating functions for word-statistics on set partitions, where (mostly) we identify a set partition with the corresponding canonical sequence (see Definition 1.3) and employ this representation to define patterns among set partitions.
