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arXiv · 2606.00772

Projective dimension of powers of cover ideal of Ferrers graphs

Do Trong Hoang·Thanh Vu
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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 $t \ge 1$.

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Do Trong Hoang, Thanh Vu. 2026-05-30. Projective dimension of powers of cover ideal of Ferrers graphs. https://arxiv.org/abs/2606.00772

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