# Questions tagged [euclidean-lattices]

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### what is the number of paths returning to 0 on the hexagonal lattice

I am looking for an estimation of the number of paths of length $n$ going from 0 to 0 on the hexagonal (or honeycomb) lattice. I can find plenty on references on self avoiding paths, but I am looking ...
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### The Monster Moonshine Module from the engineering or algorithmic point of view

From what I understand (see, e.g., this question), the Monster Moonshine Module is a kind if "third generation" (or "second quantization"?) after the Golay code (with automorphism group $M_{24}$) and ...
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### Tiling with incommensurate triangles

Say that two triangles are incommensurate if they do not share an edge length or a vertex angle, and their areas differ. Suppose you'd like to tile the plane with pairwise incommensurate triangles. I ...
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### Periodicity of density of laminated lattices

In Sphere Packings, Lattices and Groups, Conway and Sloane explore laminated lattices. If we let $X_d$ be the set of $d$-dimensional Euclidean lattices where every pair of points are separated by ...
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### Lattice basis reduction over rings of number fields

Can one use lattice basis reduction algorithms, such as LLL over (low-rank) module lattices over rings of number fields of degree greater than 1? Is there any work on lattice reductions over Euclidean ...
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### On necessary condition for no integer points in polytope

For a convex polytope $\mathcal K$ in $\Bbb R^n$ presented by $O(n^c)$ linear inequalities is it true that for $|\mathcal K\cap \Bbb Z^n|=0$ it is necessary that at least one axis of John's ellipsoid ...
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