Author:
Qureshi Ayesha Asloob,Rinaldo Giancarlo,Romeo Francesco
Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Mathematics (miscellaneous),Theoretical Computer Science
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