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Integer Partitions Under Certain Finiteness Conditions, Tim Wagner
Integer Partitions Under Certain Finiteness Conditions, Tim Wagner
Dissertations, Master's Theses and Master's Reports
This dissertation focuses on problems related to integer partitions under various finiteness restrictions. Much of our work involves the collection of partitions fitting inside a fixed partition $\lambda$, and the associated generating function $G_{\lambda}$.
In Chapter 2, we discuss the flawlessness of such generating functions, as proved by Pouzet using the Multicolor Theorem. We give novel applications of the Multicolor Theorem to re-prove flawlessness of pure $O$-sequences, and show original flawlessness results for other combinatorial sequences. We also present a linear-algebraic generalization of the Multicolor Theorem that may have far-reaching applications.
In Chapter 3, we extend a technique due to …