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arXiv · 2211.04820

The Stanley-Reisner ideal of the rook complex of polyominoes

Francesco Romeo
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Abstract

We study the properties of the rook complex $\mathcal{R}$ of a polyomino $\mathcal{P}$ seen as independence complex of a graph $G$, and the associated Stanley--Reisner ideal $I_\mathcal{R}$. In particular, we characterize the polyominoes $\mathcal{P}$ having a pure rook complex, and the ones whose Stanley--Reisner ideal has linear resolution. Furthermore, we prove that for a class of polyominoes the Castelnuovo-Mumford regularity of $I_\mathcal{R}$ coincides with the induced matching number of $G$.

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Francesco Romeo. 2022-11-09. The Stanley-Reisner ideal of the rook complex of polyominoes. https://arxiv.org/abs/2211.04820

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