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<p>This paper investigates the unimodular equivalence of sublattices in an <i>n</i>-dimensional lattice. We introduce a recursive procedure to compute the sizes of these unimodular equivalence classes when the index is a power of a prime <i>p</i>. Additionally, we derive an explicit formula for the number of cocyclic sublattices of a given index <i>m</i> and show that they constitute a single unimodular equivalence class.</p>

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On Equivalent Sublattices of an n-dimensional Lattice

  • 期刊论文

  • 发表日期：

    2026年7月5日

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  • Shikui Shang

摘要

This paper investigates the unimodular equivalence of sublattices in an n-dimensional lattice. We introduce a recursive procedure to compute the sizes of these unimodular equivalence classes when the index is a power of a prime p. Additionally, we derive an explicit formula for the number of cocyclic sublattices of a given index m and show that they constitute a single unimodular equivalence class.