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University of Illinois – Urbana-Champaign

1. DiPasquale, Michael Robert. Splines on polytopal complexes.

Degree: PhD, Mathematics, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/87949

► This thesis concerns the algebra C^{r}(\PC) of C^{r} piecewise polynomial functions (splines) over a subdivision by convex polytopes \PC of a domain Ω\subset\R^{n}. Interest in…
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Subjects/Keywords: Algebraic Splines; Commutative Algebra

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APA (6^{th} Edition):

DiPasquale, M. R. (2015). Splines on polytopal complexes. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/87949

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

DiPasquale, Michael Robert. “Splines on polytopal complexes.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/87949.

MLA Handbook (7^{th} Edition):

DiPasquale, Michael Robert. “Splines on polytopal complexes.” 2015. Web. 10 Jul 2020.

Vancouver:

DiPasquale MR. Splines on polytopal complexes. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/87949.

Council of Science Editors:

DiPasquale MR. Splines on polytopal complexes. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/87949

University of Illinois – Urbana-Champaign

2. Pechenik, Oliver A. K-theoretic Schubert calculus and applications.

Degree: PhD, Mathematics, 2016, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/92740

► A central result in algebraic combinatorics is the Littlewood-Richardson rule that governs products in the cohomology of Grassmannians. A major theme of the modern Schubert…
(more)

Subjects/Keywords: Schubert calculus; K-theory; genomic tableau; cyclic sieving; homomesy; plane partition; resonance; doppelganger

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APA (6^{th} Edition):

Pechenik, O. A. (2016). K-theoretic Schubert calculus and applications. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/92740

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

Pechenik, Oliver A. “K-theoretic Schubert calculus and applications.” 2016. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/92740.

MLA Handbook (7^{th} Edition):

Pechenik, Oliver A. “K-theoretic Schubert calculus and applications.” 2016. Web. 10 Jul 2020.

Vancouver:

Pechenik OA. K-theoretic Schubert calculus and applications. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2016. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/92740.

Council of Science Editors:

Pechenik OA. K-theoretic Schubert calculus and applications. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2016. Available from: http://hdl.handle.net/2142/92740

University of Illinois – Urbana-Champaign

3. Vichitkunakorn, Panupong. Cluster algebras and discrete integrable systems.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/97314

► This dissertation presents connections between cluster algebras and discrete integrable systems, especially T-systems and their specializations/generalizations. We give connections between the T-system or the octahedron…
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Subjects/Keywords: Cluster algebras; Discrete integrable systems

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APA (6^{th} Edition):

Vichitkunakorn, P. (2017). Cluster algebras and discrete integrable systems. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/97314

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

Vichitkunakorn, Panupong. “Cluster algebras and discrete integrable systems.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/97314.

MLA Handbook (7^{th} Edition):

Vichitkunakorn, Panupong. “Cluster algebras and discrete integrable systems.” 2017. Web. 10 Jul 2020.

Vancouver:

Vichitkunakorn P. Cluster algebras and discrete integrable systems. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/97314.

Council of Science Editors:

Vichitkunakorn P. Cluster algebras and discrete integrable systems. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/97314

University of Illinois – Urbana-Champaign

4. Anders, Katherine. Properties of digital representations.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50698

► Let 𝓐 be a finite subset of ℕ including 0 and f_𝓐(n) be the number of ways to write n=∑_{i=0}^{∞}ε_{i2}^{i}, where ε_{i}∈𝓐. The sequence ≤ ft(f_𝓐(n)))…
(more)

Subjects/Keywords: number theory; combinatorics; digital representations; generalized binary representations

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APA (6^{th} Edition):

Anders, K. (2014). Properties of digital representations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50698

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

Anders, Katherine. “Properties of digital representations.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/50698.

MLA Handbook (7^{th} Edition):

Anders, Katherine. “Properties of digital representations.” 2014. Web. 10 Jul 2020.

Vancouver:

Anders K. Properties of digital representations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/50698.

Council of Science Editors:

Anders K. Properties of digital representations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50698

University of Illinois – Urbana-Champaign

5. Searles, Dominic Nigel. Root-theoretic Young diagrams and Schubert Calculus.

Degree: PhD, Mathematics, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/87992

► A longstanding problem in algebraic combinatorics is to find nonnegative combinatorial rules for the Schubert calculus of generalized flag varieties; that is, for the structure…
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Subjects/Keywords: Root-theoretic Young diagrams; Schubert calculus; generalized flag variety; adjoint variety; Belkale-Kumar product

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APA (6^{th} Edition):

Searles, D. N. (2015). Root-theoretic Young diagrams and Schubert Calculus. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/87992

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

Searles, Dominic Nigel. “Root-theoretic Young diagrams and Schubert Calculus.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/87992.

MLA Handbook (7^{th} Edition):

Searles, Dominic Nigel. “Root-theoretic Young diagrams and Schubert Calculus.” 2015. Web. 10 Jul 2020.

Vancouver:

Searles DN. Root-theoretic Young diagrams and Schubert Calculus. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/87992.

Council of Science Editors:

Searles DN. Root-theoretic Young diagrams and Schubert Calculus. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/87992

University of Illinois – Urbana-Champaign

6. Hu, Ping. Extremal graph theory: flag algebras, Ramsey-Turan numbers, chromatic thresholds, and sparse hypergraphs.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50590

► We study problems in extremal combinatorics motivated by Turan's Theorem and Ramsey Theory. In Chapter 2, we use Flag Algebras to study these problems. With…
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Subjects/Keywords: Flag Algebras; Ramsey; Turan; Chromatic Thresholds

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APA (6^{th} Edition):

Hu, P. (2014). Extremal graph theory: flag algebras, Ramsey-Turan numbers, chromatic thresholds, and sparse hypergraphs. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50590

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

Hu, Ping. “Extremal graph theory: flag algebras, Ramsey-Turan numbers, chromatic thresholds, and sparse hypergraphs.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/50590.

MLA Handbook (7^{th} Edition):

Hu, Ping. “Extremal graph theory: flag algebras, Ramsey-Turan numbers, chromatic thresholds, and sparse hypergraphs.” 2014. Web. 10 Jul 2020.

Vancouver:

Hu P. Extremal graph theory: flag algebras, Ramsey-Turan numbers, chromatic thresholds, and sparse hypergraphs. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/50590.

Council of Science Editors:

Hu P. Extremal graph theory: flag algebras, Ramsey-Turan numbers, chromatic thresholds, and sparse hypergraphs. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50590

University of Illinois – Urbana-Champaign

7. Tian, Hongfei. On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/99314

► In this thesis we prove the existence of Jordan Decomposition in D_{G/k}, the ring of invariant differential operators on a semisimple algebraic group over a…
(more)

Subjects/Keywords: Representation theory; Positive characteristic; Invariant differential operators; Semisimple center

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APA (6^{th} Edition):

Tian, H. (2017). On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/99314

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

Tian, Hongfei. “On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/99314.

MLA Handbook (7^{th} Edition):

Tian, Hongfei. “On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic.” 2017. Web. 10 Jul 2020.

Vancouver:

Tian H. On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/99314.

Council of Science Editors:

Tian H. On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/99314

University of Illinois – Urbana-Champaign

8. O, Suil. Matchings, Connectivity, and Eigenvalues in Regular Graphs.

Degree: PhD, 0439, 2011, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/26034

► We study extremal and structural problems in regular graphs involving various parameters. In Chapter 2, we obtain the best lower bound for the matching number…
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Subjects/Keywords: Matching; Connectivity; Edge-connectivity; Eigenvalue; Regular graph; Postman; Path cover; Average (edge)-connectivity; Total Domination; Balloon; $r$-dynamic coloring

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APA (6^{th} Edition):

O, S. (2011). Matchings, Connectivity, and Eigenvalues in Regular Graphs. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/26034

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

O, Suil. “Matchings, Connectivity, and Eigenvalues in Regular Graphs.” 2011. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/26034.

MLA Handbook (7^{th} Edition):

O, Suil. “Matchings, Connectivity, and Eigenvalues in Regular Graphs.” 2011. Web. 10 Jul 2020.

Vancouver:

O S. Matchings, Connectivity, and Eigenvalues in Regular Graphs. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2011. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/26034.

Council of Science Editors:

O S. Matchings, Connectivity, and Eigenvalues in Regular Graphs. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2011. Available from: http://hdl.handle.net/2142/26034

9. Ochoa de Alaiza Gracia, Itziar. Stratifications of representations and cyclic quivers.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101520

► Given an algebraic variety X with an action of a reductive group G, geometric invariant theory splits X as the disjoint union X=X^{ss}\sqcup X^{un} of…
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Subjects/Keywords: Representations; quivers.

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APA (6^{th} Edition):

Ochoa de Alaiza Gracia, I. (2018). Stratifications of representations and cyclic quivers. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101520

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

Ochoa de Alaiza Gracia, Itziar. “Stratifications of representations and cyclic quivers.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/101520.

MLA Handbook (7^{th} Edition):

Ochoa de Alaiza Gracia, Itziar. “Stratifications of representations and cyclic quivers.” 2018. Web. 10 Jul 2020.

Vancouver:

Ochoa de Alaiza Gracia I. Stratifications of representations and cyclic quivers. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/101520.

Council of Science Editors:

Ochoa de Alaiza Gracia I. Stratifications of representations and cyclic quivers. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101520

10. Weigandt, Anna. Prism tableaux and alternating sign matrices.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101525

► A. Lascoux and M.-P. Schutzenberger introduced Schubert polynomials to study the cohomology ring of the complete flag variety Fl(C^n). Each Schubert polynomial corresponds to the…
(more)

Subjects/Keywords: Schubert polynomials; Alternating sign matrices; Durfee; Prism tableaux

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APA (6^{th} Edition):

Weigandt, A. (2018). Prism tableaux and alternating sign matrices. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101525

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

Weigandt, Anna. “Prism tableaux and alternating sign matrices.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/101525.

MLA Handbook (7^{th} Edition):

Weigandt, Anna. “Prism tableaux and alternating sign matrices.” 2018. Web. 10 Jul 2020.

Vancouver:

Weigandt A. Prism tableaux and alternating sign matrices. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/101525.

Council of Science Editors:

Weigandt A. Prism tableaux and alternating sign matrices. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101525

11. Monical, Cara. Polynomials in algebraic combinatorics.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101462

► A long-standing theme in algebraic combinatorics is to study bases of the rings of symmetric functions, quasisymmetric functions, and polynomials. Classically, these bases are homogeneous…
(more)

Subjects/Keywords: K-theoretic algebraic combinatorics; skyline fillings; Newton polytopes

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APA (6^{th} Edition):

Monical, C. (2018). Polynomials in algebraic combinatorics. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101462

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

Monical, Cara. “Polynomials in algebraic combinatorics.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/101462.

MLA Handbook (7^{th} Edition):

Monical, Cara. “Polynomials in algebraic combinatorics.” 2018. Web. 10 Jul 2020.

Vancouver:

Monical C. Polynomials in algebraic combinatorics. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/101462.

Council of Science Editors:

Monical C. Polynomials in algebraic combinatorics. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101462

12. Loeb, Sarah Jane. Coloring and covering problems on graphs.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98358

► The \emph{separation dimension} of a graph G, written π(G), is the minimum number of linear orderings of V(G) such that every two nonincident edges are…
(more)

Subjects/Keywords: Graph coloring; Graph covering

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APA (6^{th} Edition):

Loeb, S. J. (2017). Coloring and covering problems on graphs. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98358

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

Loeb, Sarah Jane. “Coloring and covering problems on graphs.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/98358.

MLA Handbook (7^{th} Edition):

Loeb, Sarah Jane. “Coloring and covering problems on graphs.” 2017. Web. 10 Jul 2020.

Vancouver:

Loeb SJ. Coloring and covering problems on graphs. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/98358.

Council of Science Editors:

Loeb SJ. Coloring and covering problems on graphs. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98358

13. Shan, Jianyun. Ideals of powers of linear forms.

Degree: PhD, 0439, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/72784

► This thesis addresses two closely related problems about ideals of powers of linear forms. In the first chapter, we analyze a problem from spline theory,…
(more)

Subjects/Keywords: Splines; fat points; free resolutions; powers of linear forms

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APA (6^{th} Edition):

Shan, J. (2015). Ideals of powers of linear forms. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/72784

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

Shan, Jianyun. “Ideals of powers of linear forms.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/72784.

MLA Handbook (7^{th} Edition):

Shan, Jianyun. “Ideals of powers of linear forms.” 2015. Web. 10 Jul 2020.

Vancouver:

Shan J. Ideals of powers of linear forms. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/72784.

Council of Science Editors:

Shan J. Ideals of powers of linear forms. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/72784

14. Curcic, Milos. Lattice polytopes with distinct pair-sums.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/42324

► Let P be a lattice polytope in R^{d}, the convex hull of a finite set in Z^{d}, and let L(P) = P intersection Z^{d} =…
(more)

Subjects/Keywords: lattice polytopes; distinct pair-sums; distinct pair-sums volume; clean tetrahedron

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APA (6^{th} Edition):

Curcic, M. (2013). Lattice polytopes with distinct pair-sums. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/42324

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

Curcic, Milos. “Lattice polytopes with distinct pair-sums.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/42324.

MLA Handbook (7^{th} Edition):

Curcic, Milos. “Lattice polytopes with distinct pair-sums.” 2013. Web. 10 Jul 2020.

Vancouver:

Curcic M. Lattice polytopes with distinct pair-sums. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/42324.

Council of Science Editors:

Curcic M. Lattice polytopes with distinct pair-sums. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/42324

University of Illinois – Urbana-Champaign

15. Kim, Byung Chan. Arithmetic of partition functions and q-combinatorics.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/15588

► Integer partitions play important roles in diverse areas of mathematics such as q-series, the theory of modular forms, representation theory, symmetric functions and mathematical physics.…
(more)

Subjects/Keywords: Partitions; Partition congruences; q-series; Modular forms; Combinatorial proof; Mock theta functions

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APA (6^{th} Edition):

Kim, B. C. (2010). Arithmetic of partition functions and q-combinatorics. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/15588

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

Kim, Byung Chan. “Arithmetic of partition functions and q-combinatorics.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/15588.

MLA Handbook (7^{th} Edition):

Kim, Byung Chan. “Arithmetic of partition functions and q-combinatorics.” 2010. Web. 10 Jul 2020.

Vancouver:

Kim BC. Arithmetic of partition functions and q-combinatorics. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/15588.

Council of Science Editors:

Kim BC. Arithmetic of partition functions and q-combinatorics. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/15588