Let $\Lambda \subseteq \mathbb{Z}^n$ be a full rank sublattice. We find an upper triangular basis matrix $B \in \mathfrak{ut}(\mathbb{Z},n)$ of $\Lambda$. Is $B$ unique up to the right action of $\mathfrak{ut}(\mathbb{Z},n) \cap GL(\mathbb{Z},n)$ (unimodular upper triangular matrices)?
Unique upper triangular basis matrix of sublattice $\Lambda \subseteq \mathbb{Z}^n$
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