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University of Oklahoma

1. Pacheco, Elizabeth. New Simple Representations of Leavitt Path Algebras.

Degree: PhD, 2019, University of Oklahoma

URL: http://hdl.handle.net/11244/323243

This thesis is about representations of Leavitt Path Algebras (LPAs). Specifically, we first generalize a previously known construction of twisted Chen modules over the Leavitt Path Algebra of a directed graph. We then give some thought to its extension to other modules, and present new classes of simple Leavitt Path Algebra modules previously unknown. These are modules generated by indicator functions of closed sets of the set of all infinite paths of a directed graph.
*Advisors/Committee Members: Ozaydin, Murad (advisor), Forester, Max (committee member), Kujawa, Jon (committee member), Przebinda, Tomasz (committee member), Havlicek, Joseph (committee member).*

Subjects/Keywords: Leavitt Path Algebras; Representation theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Pacheco, E. (2019). New Simple Representations of Leavitt Path Algebras. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/323243

Chicago Manual of Style (16^{th} Edition):

Pacheco, Elizabeth. “New Simple Representations of Leavitt Path Algebras.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed March 09, 2021. http://hdl.handle.net/11244/323243.

MLA Handbook (7^{th} Edition):

Pacheco, Elizabeth. “New Simple Representations of Leavitt Path Algebras.” 2019. Web. 09 Mar 2021.

Vancouver:

Pacheco E. New Simple Representations of Leavitt Path Algebras. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/11244/323243.

Council of Science Editors:

Pacheco E. New Simple Representations of Leavitt Path Algebras. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/323243

University of Oklahoma

2. Edwards, Craig. THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS.

Degree: PhD, 2019, University of Oklahoma

URL: http://hdl.handle.net/11244/319674

Even though the problem of counting points with integer coordinates on a (rational) polytope has connections to sophisticated mathematical topics like Algebraic K-Theory, Fourier-Dedekind Sums, Heegard-Floer Homology, Symplectic Geometry and more, the basic (open) problem(s) are easy to describe. For example the following has been an open problem for over 60 years: If a, b and c are coprime positive integers how many ways are there of obtaining a given natural number n as a sum of (nonnegative integer) multiples of a, b and c? The problem is giving an effective computable formula for this number f(n). We are able to find this formula for a particular case. Furthermore, we use a variety of techniques to find the secondary asymptotic in any case, along with an effective computable formula for the McNugget Monoid and a couple of infinite families.
*Advisors/Committee Members: Ozaydin, Murad (advisor), Schmidt, Ralf (committee member), Forester, Max (committee member), Martin, Kimball (committee member), Havlicek, Joseph (committee member).*

Subjects/Keywords: Combinatorics

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Edwards, C. (2019). THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/319674

Chicago Manual of Style (16^{th} Edition):

Edwards, Craig. “THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed March 09, 2021. http://hdl.handle.net/11244/319674.

MLA Handbook (7^{th} Edition):

Edwards, Craig. “THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS.” 2019. Web. 09 Mar 2021.

Vancouver:

Edwards C. THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Mar 09]. Available from: http://hdl.handle.net/11244/319674.

Council of Science Editors:

Edwards C. THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/319674