Numerical and Harmonic Analysis of Simplex Number Parity

<p>The primary object of this thesis is the study of periodicity in the parity of simplex numbers by number-theoretic and harmonic methods. The regular d-simplex numbers are introduced geometrically, arithmetically, and combinatorially. We demonstrate that all sequences indexing even d-simplex numbers are defined by finitely many congruences in a single modulus, and are thus quasiperiodic. We therefore show that these "even index-sequences" are particular elements in an affine space of functions, providing a natural decomposition result. We then introduce the discrete Fourier transform to construct the periodic parts of each index sequence, enabling the development of explicit forms for the ordered even d-simplex numbers for any finite dimension.</p>

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Math and Computer Science

Year dc:date.available

2026

Author dc:creator

• Hannula, Hunter DM

Contributors dc:contributor

• Daniel Rowe

• simplex numbers
• triangular numbers
• parity
• harmonic analysis
• quasiperiodic
• affine space
• Fourier analysis
• representation theory
• Algebra
• Discrete Mathematics and Combinatorics
• Harmonic Analysis and Representation
• Number Theory

Repository record dc:identifier

https://commons.nmu.edu/theses/910

OAI identifier oai:identifier

oai:commons.nmu.edu:theses-1988