# Tagged Questions

**6**

votes

**1**answer

388 views

### Higher dimensional Rubik's cube group

Since "cubes" with higher dimension than three exist I think it's natural to ask for higher dimensional Rubik's cubes. These so called hypercubes don't seem to have been described from a group ...

**1**

vote

**0**answers

74 views

### Group actions on polytopes in indefinite integer lattices

Is anything at all known about polytopes in indefinite integer lattices? I'm interested in lattice automorphisms which preserve certain polytopes of "high regularity" (e.g. cones). As a first step, ...

**0**

votes

**3**answers

273 views

### The symmetry group of $\mathbb Z^d$

Let $d \ge 1$, and consider the integer lattice $\mathbb Z^d$. This is a homogeneous space, in the manner of the Erlangan Programm.
I would like to write $\mathbb Z^d = G / H$, where $G$ is the ...

**11**

votes

**2**answers

709 views

### covers of $Z^\infty$

Is it possible to cover $Z^\infty$ (the infinite direct sum of $Z$'s with the $l_1$-metric) by a finite set of collections of subsets $U^0,...,U^n$ such that each collection $U^i$ consists of ...

**6**

votes

**3**answers

673 views

### Random Walks in $Z^2$/$Z^2$-intrinsic characterization of Euclidean distance Part II

For some context see Random Walks in $Z^2$/$Z^2$-intrinsic characterization of Euclidean distance
As per Noah's answer and JBL's comment this was false as stated. However, I think the following ...

**9**

votes

**1**answer

418 views

### Random Walks in $Z^2$/$Z^2$-intrinsic characterization of Euclidean distance

Problem: Consider a random walk on the lattice $\mathbb{Z}^2$ where on each iteration a particle either stays at its current location or moves to a neighboring vertex with probability 1/5. We start ...