Polyocollection ideals and primary decomposition of polyomino ideals

DOI10.1016/j.jalgebra.2023.11.024zbMath1530.05026arXiv2302.08337OpenAlexW4389117560MaRDI QIDQ6146654

Carmelo Cisto, Dharm Veer, Francesco Navarra

Publication date: 15 January 2024

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.08337

zbMATH Keywords

polyominoesprimary decompositionzig-zag walk

Mathematics Subject Classification ID

Polyominoes (05B50) Combinatorial aspects of commutative algebra (05E40)

Cites Work

• Nonsimple polyominoes and prime ideals
• The coordinate ring of a simple polyomino
• Binomial edge ideals and conditional independence statements
• Toric representations of algebras defined by certain nonsimple polyominoes
• Ideals generated by 2-minors, collections of cells and stack polyominoes
• Ideals generated by adjacent 2-minors
• On Gröbner basis and Cohen-Macaulay property of closed path polyominoes
• Primality of weakly connected collections of cells and weakly closed path polyominoes
• Primality of multiply connected polyominoes
• Green-Lazarsfeld condition for toric edge ideals of bipartite graphs
• Hilbert series of simple thin polyominoes
• Linearly related polyominoes
• Simple polyominoes are prime
• Algebraic properties of the coordinate ring of a convex polyomino
• Hilbert series of parallelogram polyominoes
• The \(h\)-polynomial and the rook polynomial of some polyominoes
• Gröbner bases of balanced polyominoes
• Primality of closed path polyominoes
• The Charney-Davis conjecture for simple thin polyominoes
• Primality of polyomino ideals by quadratic Gröbner basis
• Hilbert-Poincaré series and Gorenstein property for some non-simple polyominoes

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