ABSTRACT
To study statistics on a combinatorial structure it is very useful to obtain not just the enumeration of the number objects in the combinatorial structure, but to obtain results on the number of the objects in the structure that satisfy a ceratin set of conditions. For example, in Chapter 4 we considered subword-statistics on set partitions. More precisely, we studied the generating function for the number of set partitions of Pn,k according to the number occurrences of a fixed subword pattern τ . In the current chapter, we will focus on other statistics, namely “nonsubword statistics”, rather than subword statistics, where we will investigate various types of patterns that are not easy to express as subword patterns. These statistic motivated by the study of various types of statistics on the set of permutations, words and compositions, see the books of Bo´na [48] and Heubach and Mansour [138].
