Lattices from tight frames and vertex transitive graphs

Autor:	Fukshansky, Lenny, Needell, Deanna, Park, Josiah, Xin, Yuxin
Rok vydání:	2019
Předmět:	Mathematics - Combinatorics Mathematics - Metric Geometry Mathematics - Numerical Analysis Mathematics - Number Theory 11H31 52C17 42C15 05C50 05C76
Druh dokumentu:	Working Paper
Popis:	We show that real tight frames that generate lattices must be rational, and use this observation to describe a construction of lattices from vertex transitive graphs. In the case of irreducible group frames, we show that the corresponding lattice is always strongly eutactic. This is the case for the more restrictive class of distance transitive graphs. We show that such lattices exist in arbitrarily large dimensions and demonstrate examples arising from some notable families of graphs. In particular, some well-known root lattices and those related to them can be recovered this way. We discuss various properties of this construction and also mention some potential applications of lattices generated by incoherent systems of vectors. Comment: some corrections of typos made; updated bibliography
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1902.02862 Zobrazit plný text záznamu View this record from Arxiv