Regularity and the Gorenstein property of \(L\)-convex polyominoes (Q2656905)

Summary: 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. Though the main results are of algebraic nature, all proofs are combinatorial.