Some Researches Of Crossing And Nesting

Crossing and nesting are two important statistics in combinatorial mathematics. In the recent years, a large number of scholars have researched crossing and nesting on set partiton and matching. In this thesis, we will study crossing and nesting on set partition, matching and bit pairing. The main content is as follows:In the first part, we give the development of the theories of crossing and nesting."In the second part, we introduce the basic definitions and properties of set partition, match-ing, bit pairing and Dyck path.In the third part, we show some results of crossing and nesting on set partition and match-ing.In the fourth part, crossing and nesting on bit pairing are classified. We give the enumer-ative results of bit pairing on{(10)n} avoiding the crosssing of a certain type.