Hilbert series of parallelogram polyominoes

DOI10.1007/s40687-022-00323-5zbMath1492.13032arXiv2111.01907OpenAlexW3209371388MaRDI QIDQ2671740

Giancarlo Rinaldo, Francesco Romeo, Ayesha Asloob Qureshi

Publication date: 3 June 2022

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.01907

zbMATH Keywords

Gorenstein ringHilbert seriespolyominoes

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Combinatorial aspects of commutative algebra (05E40) Commutative rings defined by binomial ideals, toric rings, etc. (13F65)

Related Items (3)

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

Uses Software

• Macaulay2

Cites Work

• Regularity of join-meet ideals of distributive lattices
• The coordinate ring of a simple polyomino
• Algebraic languages and polyominoes enumeration
• Ideals generated by 2-minors, collections of cells and stack polyominoes
• A bijection for the total area of parallelogram polyominoes
• Primality of multiply connected polyominoes
• Hilbert series of simple thin polyominoes
• Combinatorics of labelled parallelogram polyominoes
• Simple polyominoes are prime
• The number of Z-convex polyominoes
• Regularity and the Gorenstein property of \(L\)-convex polyominoes
• Monomial and toric ideals associated to Ferrers graphs
• Binomial Ideals
• Monomial Algebras
• Gröbner bases of balanced polyominoes
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