Question

Conditions under which the Lattice Generated by a Subset of Lattice Vectors is Equivalent to the Original Lattice

score 136 · Answer 1 · 2020-10-28 16:22:13

Conditions under which the Lattice Generated by a Subset of Lattice Vectors is Equivalent to the Original Lattice

score 192 · Answer 2 · 2020-11-04 21:15:02

192

Views

Efficiently find at least one lattice point $(x,y)$ on hyperbola of equation $axy+bx+cy+d=0$

Published on 04 Nov 2020 - 21:15

score 45 · Answer 3 · 2026-03-27 21:35:48

45

Views

Are the singular values of matrices in $SL_2(Z)$ dense in $(0,1)$?

Published on 27 Mar 2026 - 21:35

score 48 · Answer 4 · 2020-11-08 07:25:29

48

Views

Expression of sum of squares as a sum of a specific form

Published on 08 Nov 2020 - 7:25

score 106 · Answer 5 · 2020-11-11 02:19:31

106

Views

Every distance squared between two points in $\mathbb{Z}^n$ is clearly all $\in \mathbb{N}$. Is the converse true (upto isomorphism)?

Published on 11 Nov 2020 - 2:19

score 342 · Answer 6 · 2026-03-25 17:34:19

342

Views

A semigroup $\mathbb{N}\mathcal{A}$ is saturated in $M$ if and only if $\mathbb{N}\mathcal{A}=\text{Cone}(\mathcal{A})\cap M$

Published on 25 Mar 2026 - 17:34

score 173 · Answer 7 · 2020-11-12 17:47:25

Bound on the shortest non-zero vector in any full rank n-dimensional lattice $\Lambda \subseteq \mathbb{R}^n$ with respect to the $1$-norm.

score 218 · Answer 8 · 2026-03-26 05:54:39

218

Views

Discriminant of integral basis

Published on 26 Mar 2026 - 5:54

score 140 · Answer 9 · 2026-03-25 20:35:55

140

Views

Why $\mathbb Z(\sqrt2)$ is not a lattice?

Published on 25 Mar 2026 - 20:35

score 76 · Answer 10 · 2020-12-02 10:36:10

76

Views

A Conway quadratic (form) equation in four variables

Published on 02 Dec 2020 - 10:36

score 93 · Answer 11 · 2026-03-27 07:11:57

93

Views

Intersection points convex hull and grid

Published on 27 Mar 2026 - 7:11

score 231 · Answer 12 · 2020-12-18 08:11:50

231

Views

Minkowski Theory: The embedding of fractional ideal is a full rank lattice.

Published on 18 Dec 2020 - 8:11

score 64 · Answer 13 · 2026-03-25 09:29:05

64

Views

Proving if $\gamma\in SL(2,\mathbb{Z})$ has order $6$, then $\gamma$ is conjugate to $\begin{bmatrix}0 & -1\\ 1 & 1\end{bmatrix}^{\pm1}$

Published on 25 Mar 2026 - 9:29

score 178 · Answer 14 · 2020-12-23 10:32:00

178

Views

Difference between squares of lattice points on a circle. Is this truly impossible?

Published on 23 Dec 2020 - 10:32

score 185 · Answer 15 · 2020-12-28 02:43:50

185

Views

Milnor's example for hearing the shape of drums

Published on 28 Dec 2020 - 2:43

List Question

Conditions under which the Lattice Generated by a Subset of Lattice Vectors is Equivalent to the Original Lattice

Efficiently find at least one lattice point $(x,y)$ on hyperbola of equation $axy+bx+cy+d=0$

Are the singular values of matrices in $SL_2(Z)$ dense in $(0,1)$?

Expression of sum of squares as a sum of a specific form

Every distance squared between two points in $\mathbb{Z}^n$ is clearly all $\in \mathbb{N}$. Is the converse true (upto isomorphism)?

A semigroup $\mathbb{N}\mathcal{A}$ is saturated in $M$ if and only if $\mathbb{N}\mathcal{A}=\text{Cone}(\mathcal{A})\cap M$

Bound on the shortest non-zero vector in any full rank n-dimensional lattice $\Lambda \subseteq \mathbb{R}^n$ with respect to the $1$-norm.

Discriminant of integral basis

Why $\mathbb Z(\sqrt2)$ is not a lattice?

A Conway quadratic (form) equation in four variables

Intersection points convex hull and grid

Minkowski Theory: The embedding of fractional ideal is a full rank lattice.

Proving if $\gamma\in SL(2,\mathbb{Z})$ has order $6$, then $\gamma$ is conjugate to $\begin{bmatrix}0 & -1\\ 1 & 1\end{bmatrix}^{\pm1}$

Difference between squares of lattice points on a circle. Is this truly impossible?

Milnor's example for hearing the shape of drums

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