scholarly journals Root lattices and quasicrystals

1990 ◽  
Vol 23 (19) ◽  
pp. L1037-L1041 ◽  
Author(s):  
M Baake ◽  
D Joseph ◽  
P Kramer ◽  
M Schlottmann
Keyword(s):  
Root Lattices

On the trellis complexity of root lattices and their duals

1999 ◽  
Vol 45 (6) ◽  
pp. 2168-2172 ◽  
Author(s):  
A.H. Banihashemi ◽  
I.F. Blake
Keyword(s):  
Root Lattices

scholarly journals Signed Graphs, Root Lattices, and Coxeter Groups

1994 ◽  
Vol 164 (1) ◽  
pp. 173-209 ◽  
Author(s):  
P.J. Cameron ◽  
J.J. Seidel ◽  
S.V. Tsaranov
Keyword(s):  
Coxeter Groups ◽  
Signed Graphs ◽  
Root Lattices

scholarly journals Automorphisms of certain root lattices

1983 ◽  
Vol 7 (2) ◽  
pp. 323-336 ◽  
Author(s):  
Zenji Kobayashi ◽  
Jun Morita
Keyword(s):  
Root Lattices

Root Lattices are Efficiently Generated

1997 ◽  
Vol 07 (01) ◽  
pp. 33-50
Author(s):  
Dayanand S. Rajan ◽  
Anil M. Shende
Keyword(s):  
Directed Graph ◽  
Massively Parallel ◽  
Graph Theoretic ◽  
Massively Parallel Computers ◽  
Euclidean Metrics ◽  
Theoretic Characterization ◽  
Physical Phenomena ◽  
Root Lattices ◽  
Ordered Pairs

We show that root lattices are exactly those lattices whose relevant vectors are all equal in length. We define notions of "compatibility" between the euclidean metric and the shortest path metric in the infinite directed graph induced by a subset, G, of a lattice, i.e., the directed graph whose vertices are the points in the lattice, and whose arcs are the ordered pairs (x, x+g), with x a lattice point and g a point in G. We present some ("easy to check for") criteria that a lattice and a subset of it must satisfy to ensure "compatibility" between the corresponding graphical and the euclidean metrics. We use these criteria to characterize, in more than one way, a set of "economically and efficiently generated" lattices, including root lattices. Our results include a "graph theoretic" characterization of root lattices as well. We also discuss, in brief, certain algorithmic considerations in the simulation of macroscopic physical phenomena in massively parallel computers based on suitable discretizations of euclidean space that led us to our graphical treatment of lattices.

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