Nonsimple polyominoes and prime ideals

zbMath1341.13010arXiv1502.03669MaRDI QIDQ281495

Ayesha Asloob Qureshi, Takayuki Hibi

Publication date: 11 May 2016

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

Full work available at URL: https://arxiv.org/abs/1502.03669

zbMATH Keywords

prime idealspolyominobinomial ideals

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Integral domains (13G05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Combinatorial aspects of commutative algebra (05E40)

Related Items

Toric representations of algebras defined by certain nonsimple polyominoes ⋮ 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 ⋮ 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

• Koszul bipartite graphs
• Toric ideals generalized by quadratic binomials
• Ideals generated by 2-minors, collections of cells and stack polyominoes
• Binomial ideals
• Gröbner Bases
• Monomial Ideals
• Gröbner bases of balanced polyominoes