Optimal Line Packings from Nonabelian Groups
| Autor: | John Jasper, Joseph W. Iverson, Dustin G. Mixon |
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| Rok vydání: | 2019 |
| Předmět: |
050101 languages & linguistics
Group (mathematics) 05 social sciences Equiangular polygon 02 engineering and technology Construct (python library) Representation theory Theoretical Computer Science Combinatorics Computational Theory and Mathematics Line (geometry) Turn (geometry) 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics 020201 artificial intelligence & image processing 0501 psychology and cognitive sciences Geometry and Topology Mathematics |
| Zdroj: | Discrete & Computational Geometry. 63:731-763 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-019-00084-z |
| Popis: | We use group schemes to construct optimal packings of lines through the origin. In this setting, optimal line packings are naturally characterized using representation theory, which in turn leads to a necessary integrality condition for the existence of equiangular central group frames. We conclude with an infinite family of optimal line packings using the group schemes associated with certain Suzuki 2-groups, specifically, extensions of Heisenberg groups. Notably, this is the first known infinite family of equiangular tight frames generated by representations of nonabelian groups. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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