All Questions
Tagged with lattices reference-request
62 questions
2
votes
2
answers
293
views
Equivalence relations in suplattices
I am wondering about generalisations of the concept of equivalence relations to suplattices.
Here is my motivation: Given a set $X$. The powerset $\mathcal{P}(X)$ is a suplattice. For suplattices ...
- 1,289
5
votes
1
answer
329
views
A question of compactness in the geometry of numbers
Given a star body $S \subset \mathbb{R}^n$ with the origin as interior point, the critical determinant of $S$---usually denoted as $\Delta(S)$---is the infimum of the determinants of all lattices ...
- 32.4k
2
votes
0
answers
129
views
Reference request for gluing construction of lattices
I would like to study gluing method of lattices (such as constructing Niemeier lattices from certain root lattices etc) and am looking for good references. I am aware of the book "Sphere Packings, ...
- 21
1
vote
0
answers
106
views
Information about mutant Leech lattice related to smallest perfect squared square
What happens if we follow the construction of the Leech lattice but replace the relation
$\displaystyle \sum_{n=1}^{24} n^2 = 70^2$
with the smallest perfect squared square? Explicitly, if we set ...
- 25.7k
4
votes
1
answer
297
views
Reference for subsemigroups of $\mathbb{N}^n$
A well known result about the natural numbers $\mathbb{N}$ says that for any finite subset $A \subset \mathbb{N}$ there exists $R \ge 0$ such that if $n$ is in the subgroup of $\mathbb{Z}$ generated ...
- 38.6k
2
votes
1
answer
301
views
Is there existing terminology for this technical condition on semilattices?
Given a semilattice $S$, a subset $E$, and a positive integer $n$, let $E^{[n]}$ be the set of all products of $n$-tuples in $E$. Thus $\bigcup_{n\geq 1} E^{[n]}$ is nothing but the subsemigroup of $S$...
- 354
2
votes
0
answers
243
views
Hurwitz integers and $F_4$
The Hurwitz integers are
$$
\mathcal H=
\{a+bi+cj+dk:a,b,c,d\in\mathbb Z\;\text{ or } \;a,b,c,d\in \tfrac12+\mathbb Z\}.
$$
I want to know if there is a formula, for $m\in\mathbb Z$, for the number ...
- 2,446
7
votes
2
answers
1k
views
Lattices in SOL
Consider a semi-direct product $\mathbb{Z}^2\rtimes_A\mathbb{Z}$, where $A\in SL_2(\mathbb{Z})$ and $|Tr(A)|>2$. It is clear that it is isomorphic to a lattice in the 3-dimensional solvable Lie ...
- 3,201
6
votes
1
answer
621
views
Lorentzian characterization of genus
Suppose we take the "even" indefinite lattice from page 50 in Serre A Course in Arithmetic (1973)
$$ U \; = \;
\left( \begin{array}{cc}
0 & 1 \\\
1 & 0
\end{array}
\right),$$
...
- 3,035
6
votes
2
answers
642
views
Is the square of the covering radius of an integral lattice/quadratic form always rational?
This is one of many observations from Pete L. Clark's questions on "Euclidean" quadratic forms. I sent Pete many positive integral forms that obeyed his condition. In turn, his condition turns out to ...
CommunityBot
- 1
2
votes
1
answer
661
views
Even lattices and binary codes
I have a maybe simple question about even positive-definite lattices and lattices coming from binary codes. They seemed to be used in framed vertex operator algebras.
What is known about even ...
- 45.7k
1
vote
1
answer
268
views
Do Turing Machines generates any nontrivial lattice on the set o symbols or states?
Second question, probably better: Turing Machine which generates order on the set of its states
I would like to ask ( if it is not terribly obviously wrong):
Do Turing Machine generates ...
CommunityBot
- 1