All Questions

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'...

$\DeclareMathOperator{\poly}{\mathrm{poly}}$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 ...

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} \...

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} \...

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 ...

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 ...