论文标题
广义tonnetz和离散的亚伯 - 雅各比地图
Generalized Tonnetz and discrete Abel-Jacobi map
论文作者
论文摘要
由古典欧拉（Euler）的$ tonnetz $激励，我们介绍和研究了更通用的简单综合体的组合和拓扑，$ tonn^{n，k}（l）$ of“ tonnetz type”。主要的结果是，对于广义的参数进行了足够的通用参数，tonnetz $ tonn^{n，k}（l）$是$（k-1）$ - 尺寸dimensional $ t^{k-1} $的三角剖分。在证明中，我们构建和使用“离散的Abel-Jacobi Map”的属性，该属性在torus $ t^{k-1} \ cong \ mathbb {r}^{k-1}^{k-1}/λ$中，其中$λ\ cong \ cong \ mathbb {a}} a}^a}^\ ast_ {
Motivated by classical Euler's $Tonnetz$, we introduce and study the combinatorics and topology of more general simplicial complexes $Tonn^{n,k}(L)$ of "Tonnetz type". Out main result is that for a sufficiently generic choice of parameters the generalized tonnetz $Tonn^{n,k}(L)$ is a triangulation of a $(k-1)$-dimensional torus $T^{k-1}$. In the proof we construct and use the properties of a "discrete Abel-Jacobi map", which takes values in the torus $T^{k-1} \cong \mathbb{R}^{k-1}/Λ$ where $Λ\cong \mathbb{A}^\ast_{k-1}$ is the permutohedral lattice.
