Toric representations of algebras defined by certain nonsimple polyominoes

DOI10.1216/JCA-2018-10-2-265zbMath1393.05312arXiv1511.04204OpenAlexW2963963171MaRDI QIDQ1657982

Akihiro Shikama

Publication date: 14 August 2018

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

Full work available at URL: https://arxiv.org/abs/1511.04204

zbMATH Keywords

toric idealspolyominoestoric rings

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Polyominoes (05B50) Combinatorial aspects of commutative algebra (05E40)

Related Items (9)

Primality of polyomino ideals by quadratic Gröbner basis ⋮ Hilbert-Poincaré series and Gorenstein property for some non-simple polyominoes ⋮ Primality of multiply connected 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

Cites Work

• Nonsimple polyominoes and prime ideals
• The coordinate ring of a simple polyomino
• The irreducibility of ladder determinantal varieties
• Ladder determinantal rings
• Ideals generated by 2-minors, collections of cells and stack polyominoes
• Simple polyominoes are prime
• Gröbner bases of balanced polyominoes

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