Ideals generated by 2-minors, collections of cells and stack polyominoes

DOI10.1016/j.jalgebra.2012.01.032zbMath1262.13013arXiv1203.0407OpenAlexW1977403285MaRDI QIDQ1758439

Ayesha Asloob Qureshi

Publication date: 9 November 2012

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

Full work available at URL: https://arxiv.org/abs/1203.0407

zbMATH Keywords

class groupcanonical class2-minors of a matrixinner minorsstack polyominoe

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) Other special types of modules and ideals in commutative rings (13C13)

Related Items (28)

The Charney-Davis conjecture for simple thin polyominoes ⋮ Nonsimple polyominoes and prime ideals ⋮ Rank Bounded Hibi Subrings for Planar Distributive Lattices ⋮ Toric representations of algebras defined by certain nonsimple polyominoes ⋮ Algebraic properties of the coordinate ring of a convex polyomino ⋮ Regularity and the Gorenstein property of \(L\)-convex polyominoes ⋮ Hilbert series of parallelogram polyominoes ⋮ Unnamed Item ⋮ The coordinate ring of a simple polyomino ⋮ Primality of polyomino ideals by quadratic Gröbner basis ⋮ Hilbert-Poincaré series and Gorenstein property for some non-simple polyominoes ⋮ Primality of multiply connected polyominoes ⋮ An extremal graph problem on a grid and an isoperimetric problem for polyominoes ⋮ Finite distributive lattices, polyominoes and ideals of König type ⋮ Polyocollection ideals and primary decomposition of polyomino ideals ⋮ Green-Lazarsfeld condition for toric edge ideals of bipartite graphs ⋮ Shellable simplicial complex and switching rook polynomial of frame polyominoes ⋮ Ideals generated by adjacent 2-minors ⋮ The \(h\)-polynomial and the rook polynomial of some polyominoes ⋮ Hilbert series of simple thin polyominoes ⋮ Syzygies of Hibi rings ⋮ Ideals Generated by Diagonal 2-Minors ⋮ On Gröbner basis and Cohen-Macaulay property of closed path polyominoes ⋮ Gröbner bases of balanced polyominoes ⋮ Primality of weakly connected collections of cells and weakly closed path polyominoes ⋮ Finite lattices and Gröbner bases ⋮ Linearly related polyominoes ⋮ Primality of closed path polyominoes

Cites Work

• Unnamed Item
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• Binomial edge ideals and conditional independence statements
• Determinantal rings
• Toric ideals generalized by quadratic binomials
• Ladder determinantal rings
• Primary decomposition of lattice basis ideals
• Ideals of adjacent minors
• Binomial ideals
• Ideals generated by adjacent 2-minors
• Special simplices and Gorenstein toric rings.
• Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci

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