Two-dimensional lattices with few distances
Abstract
Description
We prove that of all two-dimensional lattices of covolume 1 the hexagonal lattice has asymptotically the fewest distances. An analogous result for dimensions 3 to 8 was proved in 1991 by Conway and Sloane. Moreover, we give a survey of some related literature, in particular progress on a conjecture from 1995 due to Schmutz Schaller.
21 pages, final version, accepted for publication in L'Enseignement Mathématique
21 pages, final version, accepted for publication in L'Enseignement Mathématique