Geodesic
Regularity and the Gorenstein property of \(L\)-convex polyominoes
Viviana Ene1 ; Jürgen Herzog2 ; Ayesha Asloob Qureshi3 ; Francesco Romeo4
1Ovidius University
2Universität Duisburg-Essen
3Sabanci university
4University of Trento
The electronic journal of combinatorics, Tome 28 (2021) no. 1
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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.
DOI : 10.37236/9531
Classification : 05E40, 05B50, 13C05, 13C14, 13D02, 13P10, 14M12
Mots-clés : ideal of \(t\)-minors, 2-minors of a matrix, inner minors

Viviana Ene  1   ; Jürgen Herzog  2   ; Ayesha Asloob Qureshi  3   ; Francesco Romeo  4

1 Ovidius University
2 Universität Duisburg-Essen
3 Sabanci university
4 University of Trento 
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     author = {Viviana Ene and J\"urgen Herzog and Ayesha Asloob Qureshi and Francesco Romeo},
     title = {Regularity and the {Gorenstein} property of {\(L\)-convex} polyominoes},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {1},
     doi = {10.37236/9531},
     zbl = {1460.05205},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9531/}
}
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Viviana Ene; Jürgen Herzog; Ayesha Asloob Qureshi; Francesco Romeo. Regularity and the Gorenstein property of \(L\)-convex polyominoes. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/9531

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