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Mathematics

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University of Texas Rio Grande Valley

Theses/Dissertations

Number theory

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Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen Dec 2018

Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen

Theses and Dissertations

We show for a prime power number of parts m that the first differences of partitions into at most m parts can be expressed as a non-negative linear combination of partitions into at most m – 1 parts. To show this relationship, we combine a quasipolynomial construction of p(n,m) with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of p(n,m) and the new partition identity. We extend these results by establishing conditions for when partitions of n with parts coming from …


Problem Book On Higher Algebra And Number Theory, Ryanto Putra May 2017

Problem Book On Higher Algebra And Number Theory, Ryanto Putra

Theses and Dissertations

This book is an attempt to provide relevant end-of-section exercises, together with their step-by-step solutions, to Dr. Zieschang's classic class notes Higher Algebra and Number Theory. It's written under the notion that active hands-on working on exercises is an important part of learning, whereby students would see the nuance and intricacies of a math concepts which they may miss from passive reading. The problems are selected here to provide background on the text, examples that illuminate the underlying theorems, as well as to fill in the gaps in the notes.


On Cubic Multisections, Andrew Alaniz Aug 2013

On Cubic Multisections, Andrew Alaniz

Theses and Dissertations - UTB/UTPA

In this thesis, a systematic procedure is given for generating cubic multi-sections of Eisenstein series. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. The resulting series are shown to be rational functions of the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations.