Geodesic
Lattices from tight frames and vertex transitive graphs
Lenny Fukshansky1 ; Deanna Needell ; Josiah Park ; Yuxin Xin
1Claremont McKenna College
The electronic journal of combinatorics, Tome 26 (2019) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We show that real tight frames that generate lattices must be rational. In the case of irreducible group frames, we show that the corresponding lattice is always strongly eutactic. We use this observation to describe a construction of strongly eutactic lattices from vertex transitive graphs. We show that such lattices exist in arbitrarily large dimensions and discuss some examples arising from complete graphs, product graphs, as well as some other notable examples 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.
DOI : 10.37236/8502
Classification : 11H31, 52C17, 42C15, 05C50, 05C76
Mots-clés : tight frames, strongly eutactic configurations, irreducible matrix groups, vertex transitive graphs

Lenny Fukshansky  1   ; Deanna Needell    ; Josiah Park    ; Yuxin Xin 

1 Claremont McKenna College 
@article{10_37236_8502,
     author = {Lenny Fukshansky and Deanna Needell and Josiah Park and Yuxin Xin},
     title = {Lattices from tight frames and vertex transitive graphs},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {3},
     doi = {10.37236/8502},
     zbl = {1443.11131},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8502/}
}
TY  - JOUR
AU  - Lenny Fukshansky
AU  - Deanna Needell
AU  - Josiah Park
AU  - Yuxin Xin
TI  - Lattices from tight frames and vertex transitive graphs
JO  - The electronic journal of combinatorics
PY  - 2019
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/8502/
DO  - 10.37236/8502
ID  - 10_37236_8502
ER  - 
%0 Journal Article
%A Lenny Fukshansky
%A Deanna Needell
%A Josiah Park
%A Yuxin Xin
%T Lattices from tight frames and vertex transitive graphs
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8502/
%R 10.37236/8502
%F 10_37236_8502
Lenny Fukshansky; Deanna Needell; Josiah Park; Yuxin Xin. Lattices from tight frames and vertex transitive graphs. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8502

Cité par Sources :