Hilbert series of parallelogram polyominoes

Asloob Topaçoğlu, Ayesha and Rinaldo, Giancarlo and Romeo, Francesco (2022) Hilbert series of parallelogram polyominoes. Research in the Mathematical Sciences, 9 (2). ISSN 2522-0144 (Print) 2197-9847 (Online)

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We present a conjecture about the reduced Hilbert series of the coordinate ring of a simple polyomino in terms of particular arrangements of non-attacking rooks that can be placed on the polyomino. By using a computational approach, we prove that the above conjecture holds for all simple polyominoes up to rank 11. In addition, we prove that the conjecture holds true for the class of parallelogram polyominoes, by looking at those as simple planar distributive lattices. Finally, we give a combinatorial interpretation of the Gorensteinness of parallelogram polyominoes.
Item Type: Article
Uncontrolled Keywords: Distributive lattices; Gorenstein; Hilbert series; Parallelogram polyominoes
Subjects: Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Ayesha Asloob Topaçoğlu
Date Deposited: 23 Jun 2022 14:34
Last Modified: 22 Aug 2022 19:56
URI: https://research.sabanciuniv.edu/id/eprint/42838

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