List questions from integer-lattices

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58

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Problem from Red Book

Published on 09 Apr 2022 - 1:30

39

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Second group cohomology $H^2(\mathbb Z^n, \mathbb C^*)=?$

Published on 13 Apr 2022 - 13:14

75

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Enumerating the square equivalent classes

Published on 15 Apr 2022 - 21:48

212

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In which dimensions do there exist inequivalent lattices with the same theta function?

Published on 26 Mar 2026 - 19:15

74

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Finding an isomorphism between an infinite tree and a subgraph of $\mathbb{Z}^3$

Published on 25 Mar 2026 - 7:48

58

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Voronoi relevant vectors VS shortest vector

Published on 25 Mar 2026 - 17:25

583

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Check if two bases form the same lattice

Published on 25 Apr 2022 - 12:34

91

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Combinatorial isoperimetric inequality

Published on 25 Apr 2022 - 21:00

44

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If $\omega_1/\omega_2$ is not real then there exists a constant $k >0$ such that for all $n,m \in \mathbb Z$, $|m\omega_1+n\omega_2| \geq k(|m|+|n|)$

Published on 02 May 2022 - 7:40

145

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Number of lattice points $7$ units away

Published on 13 May 2022 - 13:48

96

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Proving that $a_i,b_i \to 0$ where $a_{i+1} := |b_i - a_i|$ and $b_{i+1} := |a_i - a_{i+1}|$?

Published on 20 May 2022 - 8:13

450

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Why is a unimodular lattice self-dual?

Published on 25 Mar 2026 - 11:19

59

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Integral matrices up to unimodular matrices

Published on 08 Jun 2022 - 10:40

111

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Lattices are precisely the symmetric bilinear form modules

Published on 15 Jun 2022 - 13:39

List Question

A shortest k-sequence need not form a basis of the lattice

Problem from Red Book

Second group cohomology $H^2(\mathbb Z^n, \mathbb C^*)=?$

Enumerating the square equivalent classes

In which dimensions do there exist inequivalent lattices with the same theta function?

Finding an isomorphism between an infinite tree and a subgraph of $\mathbb{Z}^3$

Voronoi relevant vectors VS shortest vector

Check if two bases form the same lattice

Combinatorial isoperimetric inequality

If $\omega_1/\omega_2$ is not real then there exists a constant $k >0$ such that for all $n,m \in \mathbb Z$, $|m\omega_1+n\omega_2| \geq k(|m|+|n|)$

Number of lattice points $7$ units away

Proving that $a_i,b_i \to 0$ where $a_{i+1} := |b_i - a_i|$ and $b_{i+1} := |a_i - a_{i+1}|$?

Why is a unimodular lattice self-dual?

Integral matrices up to unimodular matrices

Lattices are precisely the symmetric bilinear form modules

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