Date of Award
5-2026
Degree Type
Thesis
Degree Name
Master of Science
Department
Math and Computer Science
Program
Mathematics (MS)
First Advisor/Chairperson
Daniel Rowe
Abstract
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.
Recommended Citation
Hannula, Hunter DM, "Numerical and Harmonic Analysis of Simplex Number Parity" (2026). All NMU Master's Theses. 910.
https://commons.nmu.edu/theses/910
Access Type
Open Access
Fixed Signature Page (added thesis title, fixed Dept. Head and Grad Dean titles)
Hunter Hannula.pdf (33 kB)
Signed Signature Page
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Harmonic Analysis and Representation Commons, Number Theory Commons