Characterizing the properties of specific binomial coefficients in congruence relations

<p>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.</p>

Name thesis:degree_name

Master of Arts (MA)

Level thesis:degree_level

Open Access Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2015

Author dc:creator

• Russ, Tyler Robert

Contributors dc:contributor

• Andrew Wilfong, Ph.D., Chair
• David Folk, Ph.D.
• Jayakumar Ramanathan, Ph.D.

• Binomial coefficients
• number theory
• Mathematics

Repository record dc:identifier

https://commons.emich.edu/theses/640

OAI identifier oai:identifier

oai:commons.emich.edu:theses-2019