论文标题
嵌入维度三的最长和最短因素化
Longest and Shortest Factorizations in Embedding Dimension Three
论文作者
论文摘要
对于数值单差$ \ langle n_1，\ dots，n_k \ rangle $ minimally $ n_1，\ dots，n_k \ in \ at \ m athbb {n} $，带有$ n_1 <\ n_1 <\ cdots <n_k $，<n_k $，$ x $ x $ x $ x $ x $ x $ x $ l（）分别遵循身份$ l（x + n_1）= l（x） + 1 $和$ \ ell（x + n_k）= \ ell（x） + 1 $ for足够大元素$ x $。我们表征了这些身份在嵌入尺寸的所有数值单体的所有元素中都存在的表征。
For a numerical monoid $\langle n_1, \dots, n_k \rangle$ minimally generated by $n_1, \dots, n_k \in \mathbb{N}$ with $n_1 < \cdots < n_k$, the longest and shortest factorization lengths of an element $x$, denoted as $L(x)$ and $\ell(x)$, respectively, follow the identities $L(x+n_1) = L(x) + 1$ and $\ell(x+n_k) = \ell(x) + 1$ for sufficiently large elements $x$. We characterize when these identities hold for all elements of numerical monoids of embedding dimension three.
