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Results tagged with lattices
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user 129064
Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
5
votes
The smallest volume possible for a lattice with integer distances?
The smallest determinant question is answered in the lemma of section 5 in Conway & Sloane's Lattices with Few Distances. …
- 401
14
votes
1
answer
476
views
Geometric explanation for coincidence in lengths of 16-dimensional even unimodular lattices?
Collected results
The lattices are even.
$D_{n}^{+}$ is a lattice when $n\equiv0\pmod{2}$. … Motivation
In Four-Dimensional Lattices With the Same Theta Series, Conway and Sloane construct an explicit length-preserving bijection between isospectral lattices (changing the sign of the first coordinate …
- 401
3
votes
Geometric explanation for coincidence in lengths of 16-dimensional even unimodular lattices?
Outline
Allowing for rotations and reflections of cosets, it's straightforward to see that the cosets of the respective lattices are congruent upon breaking up the lattices into 4D chunks, primarily thanks … Details
For notational convenience, I set up a semiring in which two lattices are equivalent iff they can be split along cosets which can be rotated/reflected into each other. …
- 401