Primality of polyomino ideals by quadratic Gröbner basis

DOI10.1002/mana.202000252zbMath1522.05503arXiv2005.08758OpenAlexW4210366969MaRDI QIDQ6093943

Giancarlo Rinaldo, Francesco Romeo, Carla Mascia

Publication date: 9 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.08758

zbMATH Keywords

Gröbner basispolyomino ideals

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Structure, classification theorems for modules and ideals in commutative rings (13C05) Polyominoes (05B50) Combinatorial aspects of commutative algebra (05E40)

Related Items (5)

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 ⋮ On Gröbner basis and Cohen-Macaulay property of closed path polyominoes ⋮ Primality of weakly connected collections of cells and weakly closed path polyominoes

Cites Work

• Unnamed Item
• Nonsimple polyominoes and prime ideals
• The coordinate ring of a simple polyomino
• The irreducibility of ladder determinantal varieties
• Determinantal rings
• Ladder determinantal rings
• Toric representations of algebras defined by certain nonsimple polyominoes
• Ideals generated by 2-minors, collections of cells and stack polyominoes
• Gröbner bases and Stanley decompositions of determinantal ideals
• Ideals of adjacent minors
• Binomial ideals
• Primality of multiply connected polyominoes
• Simple polyominoes are prime
• Ideals of generic minors
• Binomial Ideals
• Gröbner bases of balanced polyominoes

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