All Questions
10 questions
1
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0
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51
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Coarse-graining a hypergraph
$\DeclareMathOperator{\poly}{\mathrm{poly}}$I have asked this question on math.SE here, but couldn't get a satisfactory answer. I have also asked a related question on math overflow here, but haven't ...
- 277
1
vote
0
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68
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Finding a particular kind of basis of subgroup of a lattice generated by non-negative part
For $\mathbf v=(v_1,\ldots,v_n)\in \mathbb Z^n$, let $\operatorname{supp}(\mathbf v):=\{j: v_j \ne 0\}$. For a subset $X$ of $\mathbb Z^n$, define $\operatorname{supp}(X):=\bigcup_{\mathbf v \in X} \...
- 412
1
vote
0
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124
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Number of lattice points in a structural symmetric convex body
Let $f$ is a convex symmetric function on the interval $[-a,a]$, i.e., $f(-x)=f(x)$ for $\forall \, x\in [-a,a]$. Then we consider a $n$-dimensional convex body in Euclidean space
\begin{equation}
\...
- 550
4
votes
1
answer
293
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Number of points in a lattice and an oblong box
I have a very simple question in geometry of numbers. (It is a slight modification of Counting points on the intersection of a box and a lattice .) There's a bound I can easily prove, and it's good ...
- 20.2k
1
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0
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229
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Geometric interpretation of k-th power of first n natural numbers and summation using Pick's theorem
I want to know is there any interesting properties of this approach or generalization to find $S_k(n)=1^k+2^k+3^k+\cdots+n^k$ by using Pick's Theorem $S=i+\tfrac{b}{2}-1$, where $i$-number of ...
- 19
11
votes
1
answer
442
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Chromatic number of Voronoi diagrams of lattices
Let $L$ be a Euclidean lattice. Define a graph whose vertex set is $L$ and where two points $x,y\in L$ are declared to be adjacent whenever the cells of $x$ and $y$ in the Voronoi diagram of $L$ have ...
- 32.5k
7
votes
1
answer
271
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How "accidental" are equalities between parts of Ehrhart quasi-polynomials? When do they persist to Euler-Maclaurin?
Background
What I think of Ehrhart theory (http://en.wikipedia.org/wiki/Ehrhart_polynomial) asserts that if we take a lattice polytope $P$, and count the number of lattice points in the $t$th ...
- 2,372
2
votes
0
answers
89
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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, I'...
- 393
0
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0
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113
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Question regarding contiguous forms
I read about contiguous forms in Achill Scürmann's thesis on positive quadratic forms. I am wondering about one aspect of the Voronoi algorithm presented in there, that enumerates all arithmetically ...
- 149
7
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2
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963
views
Maximal number of edges and triangular cells for n points in a triangular lattice
Consider a subset of $n$ points in an equilateral triangular lattice. Draw all the edges between nearest-neighbor points.
What is the maximum, over all such subsets, of the number of edges? This ...
- 567