2024/04/05 by Matsuo, Atsushi, Shimakura, Hiroki
#Combinatorics (math.CO) #FOS: Mathematics #Primary 11H06 #Secondary 17B22
paper · doi:10.48550/arxiv.2404.03897
A series of integral lattices parametrised by integers k,m,n are introduced and investigated, where n is the rank of the lattice, including the root lattices described in a uniform way and unimodular lattices such as the Niemeier lattices of type A24 and D24. The lattices are characterised by means of a sublattice isomorphic to the root lattice of type An-1. A sufficient condition for existence of an orthogonal k-frame of such a lattice is given in terms of symmetric 2-designs.