Exploring noncrossing partitions

Specialeforsvar: Peter Low Kildeager

Titel: Exploring noncrossing partitions 

Abstract: This thesis studies noncrossing partitions, a well-known object in combinatorics. We explore the relationship between noncrossing partitions and ordered trees, and we introduce a generalization of noncrossing partitions to arbitrary point sets, where we find patterns in the sets with minimal and maximal partition sizes. We examine properties of the volumes of noncrossing partitions, and also find a congruence pattern in the enumeration function of noncrossing partitions with distinct sizes. Finally we also examine subsets of noncrossing partitions and establish a connection between the number of partitions with blocks of size $k$ and the number of partitions with blocks whose sizes are divisible by $k-1$. 

Vejledere: Søren Eilers, Mikkel Abrahamsen, DIKU
Censor:     Peter Beelen, DTU