Year: 2026
Type: preprint
Abstract: In this work, we enumerate the ternary perfect forms over all imaginary quadratic fields of absolute discriminant up to $91$ and study the number and combinatorial types of their associated polytopes. We prove a bound on the number of combinatorial types that can arise regardless of the discriminant. We analyze the data and make several observations concerning the number and complexity of the perfect forms that arise in the scope of our calculation.
Source: arXiv (Cornell University)
Authors: Parker, Zachary, Yasaki, Dan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214575257