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arXiv · 2210.12665

Non-simple polyominoes of K\H{o}nig type and their canonical module

Rodica Dinu·Francesco Navarra
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Abstract

We study the K\H{o}nig type property for non-simple polyominoes. We prove that, for closed path polyominoes, the polyomino ideals are of K\H{o}nig type, extending the results of Herzog and Hibi for simple thin polyominoes. As an application of this result, we give a combinatorial interpretation for the canonical module of the coordinate ring of a sub-class of closed path polyominoes, namely circle closed path polyominoes. In this case, we compute also the Cohen-Macaulay type and we show that $K[\mathcal{P}]$ is a level ring.

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Rodica Dinu, Francesco Navarra. 2022-10-23. Non-simple polyominoes of K\H{o}nig type and their canonical module. https://doi.org/10.1016/j.jalgebra.2025.02.034

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