Similarity submodules and root systems in four dimensions
Michael Baake, Robert V. Moody
Abstract
Lattices and Z-modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We classify such self-similar images according to their indices for certain 4D examples that are related to 4D root systems, both crystallographic and non-crystallographic. We encapsulate their statistics in terms of Dirichlet series generating functions and derive some of their asymptotic properties.
Create a lesson
Related papers
The Spherical Hadwiger Theorem
Suijie Wang, Shengguo Wu
Linear isoperimetric filling inequalities in Hadamard spaces at and above the asymptotic rank
Jonas W. Peteranderl
Isometry invariant valuations on spherical polytopes
Jonas Knoerr
The Kernel Deficit Dominates Twice the Hull Deficit: A Sharp Strengthening of Nakano's Inequality
Dakota Charles Baker
In Search of Melchior's Ordinary Points
Jonathan Lenchner, Rik Sengupta
Volume and Projection Inequalities II: Determinants and Lp-Sums
Matthieu Fradelizi, Auttawich Manui, Cheikh Saliou Ndiaye et al.