论文标题
多摩尼亚群岛的Rook综合体的Stanley-Reisner理想
The Stanley-Reisner ideal of the rook complex of polyominoes
论文作者
论文摘要
我们研究了polyomino $ \ Mathcal {p} $的Rook Complex $ \ MATHCAL {R} $的属性，被视为图形$ G $的独立综合体，以及相关的Stanley-reisner-Reisner-Reisner Ideal $ i_ \ Mathcal {r} $。特别是，我们表征了具有纯净的Rook综合体的polyominoes $ \ MATHCAL {P} $，而Stanley-Reisner Ideasal具有线性分辨率。此外，我们证明，对于一类Polyominoes，Castelnuovo-Mumford的规律性为$ i_ \ Mathcal {r} $与诱导的匹配数量的$ G $相吻合。
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 $G$.
