Two-dimensional lattices with few distances
|Title:||Two-dimensional lattices with few distances||Authors:||Moree, Pieter
|Permanent link:||http://hdl.handle.net/10197/7958||Date:||Jun-2006||Online since:||2016-09-16T11:42:32Z||Abstract:||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.||Type of material:||Journal Article||Publisher:||European Mathematical Society||Journal:||L'Enseignement Mathematique||Volume:||52||Issue:||2||Start page:||361||End page:||380||Keywords:||Schmutz Schaller conjecture; Population fraction; Binary quadratic forms; Erdős number||DOI:||10.5169/seals-2239||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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