Isometries are ubiquitous in nature; isometries of discrete (quantized) objects---abstracted as the group of isometries of $\mathbb{Z}^n$ denoted by $\mathsf{ISO}(\mathbb{Z}^n)$---are important concepts in the computational world. In this paper, we compute various isometric invariances which mathematically are orbit-computation problems under various isometry-subgroup actions $H \curvearrowright \mathbb{Z}^n, H \leq \mathsf{ISO}(\mathbb{Z}^n)$... (read more)

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