单模超图覆盖理想幂的V数
V-numbers of powers of cover ideals of unimodular hypergraphs
AI总结：
该研究证明了单模超图覆盖理想幂的局部v数、特定范围的全局v数，以及任意树覆盖理想幂的全局v数均随幂次t呈线性变化。
AI中文摘要：
设H为单模超图，其覆盖理想记为J(H)。我们证明：对所有t≥1，J(H)^t的局部v数关于t呈线性关系；进一步证明，对所有t≥n-1，J(H)^t的全局v数关于t呈线性关系；最后证明，对所有t≥1，任意树的覆盖理想幂的全局v数关于t呈线性关系。
英文摘要：
Let $H$ be a unimodular hypergraph with cover ideal $J(H)$. We prove that the local $v$-numbers of $J(H)^t$ are linear in $t$ for all $t\ge1$. We further show that the global $v$-number of $J(H)^t$ is linear in $t$ for all $t\ge n-1$. Finally, we prove that the global $v$-number of the powers of the cover ideal of any tree is linear in $t$ for all $t\ge1$.
