Abstract:Let $\lambda = (\lambda_1, \ldots, \lambda_n)$ be a partition with $\lambda_1 = m$. Denote by $J_\lambda$ the cover ideal in the polynomial ring \( S = k[x_1, \ldots, x_n, y_1, \ldots, y_m] \) associated to the Ferrers graph corresponding to $\lambda$. Let $d(\lambda)$ denote the number of distinct parts of $\lambda$. We prove that \[ \operatorname{pd}(S/J_\lambda^t) = \min\{t,\; d(\lambda)\} + 1 \] for all $t \ge 1$.
From: Thanh Vu [view email]
[v1]
Sat, 30 May 2026 15:29:29 UTC (8 KB)
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