2013/06/11 by Maciej Borodzik, Borodzik, Maciej, Danny Nguyen +3
Computer Science · Engineering · Materials Science · #32A27 #52C17 #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Quasicrystal Structures and Properties #graph theory and CDMA systems #primary: 52C10 #secondary: 52C15
paper · pdf · doi:10.48550/arxiv.1306.2644
openalex publication_date 2013/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When ℤd is represented as a finite disjoint union of translated integer sublattices, the translated sublattices must possess some special properties. Such a representation is called a lattice tiling. We develop a theoretical framework, based on multiple residues and dual groups, to provide a set of necessary and sufficient conditions for such a lattice tiling to exist. We also investigate the question of when a lattice tiling must possess at least two translated sublattices which are translates of one another.