Regularity and Gorenstein property of the $L$-convex Polyominoes
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.08189
- arXiv:
- arXiv:1911.08189
- Bibcode:
- 2019arXiv191108189E
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Combinatorics