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Articles 1 - 4 of 4
Full-Text Articles in Algebra
The Beautiful Math Of Everything And You Included, E. Ozie
The Beautiful Math Of Everything And You Included, E. Ozie
The STEAM Journal
This a reflection on how there is beautiful math to everything. An author's interpretation of matrices and mechanics in its relationship to someone's identity.
On The Mysteries Of Interpolation Jack Polynomials, Havi Ellers
On The Mysteries Of Interpolation Jack Polynomials, Havi Ellers
HMC Senior Theses
Interpolation Jack polynomials are certain symmetric polynomials in N variables with coefficients that are rational functions in another parameter k, indexed by partitions of length at most N. Introduced first in 1996 by F. Knop and S. Sahi, and later studied extensively by Sahi, Knop-Sahi, and Okounkov-Olshanski, they have interesting connections to the representation theory of Lie algebras. Given an interpolation Jack polynomial we would like to differentiate it with respect to the variable k and write the result as a linear combination of other interpolation Jack polynomials where the coefficients are again rational functions in k. In this …
A Coherent Proof Of Mac Lane's Coherence Theorem, Luke Trujillo
A Coherent Proof Of Mac Lane's Coherence Theorem, Luke Trujillo
HMC Senior Theses
Mac Lane’s Coherence Theorem is a subtle, foundational characterization of monoidal categories, a categorical concept which is now an important and popular tool in areas of pure mathematics and theoretical physics. Mac Lane’s original proof, while extremely clever, is written somewhat confusingly. Many years later, there still does not exist a fully complete and clearly written version of Mac Lane’s proof anywhere, which is unfortunate as Mac Lane’s proof provides very deep insight into the nature of monoidal categories. In this thesis, we provide brief introductions to category theory and monoidal categories, and we offer a precise, clear development of …
Stationary Distribution Of Recombination On 4x4 Grid Graph As It Relates To Gerrymandering, Camryn Hollarsmith
Stationary Distribution Of Recombination On 4x4 Grid Graph As It Relates To Gerrymandering, Camryn Hollarsmith
Scripps Senior Theses
A gerrymandered political districting plan is used to benefit a group seeking to elect more of their own officials into office. This practice happens at the city, county and state level. A gerrymandered plan can be strategically designed based on partisanship, race, and other factors. Gerrymandering poses a contradiction to the idea of “one person, one vote” ruled by the United States Supreme Court case Reynolds v. Sims (1964) because it values one demographic’s votes more than another’s, thus creating an unfair advantage and compromising American democracy. To prevent the practice of gerrymandering, we must know how to detect a …