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arXiv · 1911.08189

Regularity and Gorenstein property of the $L$-convex Polyominoes

Viviana Ene·Jürgen Herzog·Ayesha Asloob Qureshi·Francesco Romeo
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Abstract

We study the coordinate ring of an $L$-convex polyomino, determine its regularity in terms of the maximal number of rooks that can be placed in the polyomino. We also characterize the Gorenstein $L$-convex polyominoes and those which are Gorenstein on the punctured spectrum, and compute the Cohen--Macaulay type of any $L$-convex polyomino in terms of the maximal rectangles covering it.

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Viviana Ene, Jürgen Herzog, Ayesha Asloob Qureshi, Francesco Romeo. 2019-11-19. Regularity and Gorenstein property of the $L$-convex Polyominoes. https://arxiv.org/abs/1911.08189

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