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Eastern Michigan University

1. Russ, Tyler Robert. Characterizing the properties of specific binomial coefficients in congruence relations.

Degree: MA, Mathematics, 2015, Eastern Michigan University

URL: http://commons.emich.edu/theses/640

The number theoretic conjecture we examine in this paper originates when trying to construct a characterizable generating set for the complex cobordism polynomial ring. To date there is no efficient, universal method for characterizing such a generating set. Wilfong conjectures that smooth projective toric varieties can act as these generators [7]. Toric varieties are related to polytopes by a bijective correspondence. Studying the combinatorial structure of these polytopes is much more manageable than studying properties of toric varieties directly. This gives rise to the number theoretic conjecture considered here. A proof of this number theoretic conjecture would in turn prove the conjecture that smooth projective toric varieties provide a generating set for the complex cobordism polynomial ring. Here, we do not provide a complete proof of the number theoretic conjecture, rather we give more evidence to the conjecture, building on prior work of Wilfong and Parry.
*Advisors/Committee Members: Andrew Wilfong, Ph.D., Chair, David Folk, Ph.D., Jayakumar Ramanathan, Ph.D..*

Subjects/Keywords: Binomial coefficients; number theory; Mathematics

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APA (6^{th} Edition):

Russ, T. R. (2015). Characterizing the properties of specific binomial coefficients in congruence relations. (Masters Thesis). Eastern Michigan University. Retrieved from http://commons.emich.edu/theses/640

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

Russ, Tyler Robert. “Characterizing the properties of specific binomial coefficients in congruence relations.” 2015. Masters Thesis, Eastern Michigan University. Accessed March 20, 2019. http://commons.emich.edu/theses/640.

MLA Handbook (7^{th} Edition):

Russ, Tyler Robert. “Characterizing the properties of specific binomial coefficients in congruence relations.” 2015. Web. 20 Mar 2019.

Vancouver:

Russ TR. Characterizing the properties of specific binomial coefficients in congruence relations. [Internet] [Masters thesis]. Eastern Michigan University; 2015. [cited 2019 Mar 20]. Available from: http://commons.emich.edu/theses/640.

Council of Science Editors:

Russ TR. Characterizing the properties of specific binomial coefficients in congruence relations. [Masters Thesis]. Eastern Michigan University; 2015. Available from: http://commons.emich.edu/theses/640