Physical Sciences and Mathematics Commons^™

Analytic And Topological Combinatorics Of Partition Posets And Permutations, Jiyoon Jung

Theses and Dissertations--Mathematics

In this dissertation we first study partition posets and their topology. For each composition c we show that the order complex of the poset of pointed set partitions is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module of a border strip associated to the composition. We also study the filter of pointed set partitions generated by knapsack integer partitions. In the second half of this dissertation we study descent …