Hilbert series of simple thin polyominoes

DOI10.1007/s10801-021-01017-xzbMath1480.13014arXiv2006.08512OpenAlexW3126978549MaRDI QIDQ2240736

Giancarlo Rinaldo, Francesco Romeo

Publication date: 4 November 2021

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.08512

zbMATH Keywords

Gorenstein algebrasHilbert-Poincaré seriesrook polynomialsimple polyominoes

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Polyominoes (05B50)

Related Items (8)

The Charney-Davis conjecture for simple thin polyominoes ⋮ Hilbert series of parallelogram polyominoes ⋮ 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 ⋮ The \(h\)-polynomial and the rook polynomial of some 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

• Bounds on the regularity of toric ideals of graphs
• The coordinate ring of a simple polyomino
• Hilbert functions of graded algebras
• Toric representations of algebras defined by certain nonsimple polyominoes
• Ideals generated by 2-minors, collections of cells and stack polyominoes
• Primality of multiply connected polyominoes
• Simple polyominoes are prime
• Special simplices and Gorenstein toric rings.
• Regularity and the Gorenstein property of \(L\)-convex polyominoes
• Binomial Ideals
• The Geometry of Syzygies
• Monomial Algebras
• Gröbner bases of balanced polyominoes
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