Primality of multiply connected polyominoes

DOI10.1215/00192082-8591560zbMath1497.05033arXiv1907.08438OpenAlexW3040506021MaRDI QIDQ2192221

Carla Mascia, Giancarlo Rinaldo, Francesco Romeo

Publication date: 13 August 2020

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.08438

zbMATH Keywords

polyominoes with holeszig-zag walk

Mathematics Subject Classification ID

Graded rings (13A02) Polyominoes (05B50) Combinatorial aspects of commutative algebra (05E40)

Related Items (10)

Regularity and the Gorenstein property of \(L\)-convex polyominoes ⋮ Hilbert series of parallelogram polyominoes ⋮ Primality of polyomino ideals by quadratic Gröbner basis ⋮ Hilbert-Poincaré series and Gorenstein property for some non-simple polyominoes ⋮ Polyocollection ideals and primary decomposition of polyomino ideals ⋮ Shellable simplicial complex and switching rook polynomial of frame polyominoes ⋮ Hilbert series of simple thin polyominoes ⋮ 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 closed path polyominoes

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Nonsimple polyominoes and prime ideals
• The coordinate ring of a simple polyomino
• Toric representations of algebras defined by certain nonsimple polyominoes
• Ideals generated by 2-minors, collections of cells and stack polyominoes
• Simple polyominoes are prime
• Gröbner bases of balanced polyominoes

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