Year: 2025
Type: article
Abstract: Polyomino ideals, defined as the ideals generated by the inner $2$-minors of a polyomino, are a class of binomial ideals whose algebraic properties are closely related to the combinatorial structure of the underlying polyomino. We provide a unified account of recent advances on two central themes: the characterization of prime polyomino ideals and the emerging connection between the Hilbert–Poincaré series and Gorensteinness of \(K[\Pc]\) with the classical rook theory. Some further related properties, as radicality, primary decomposition, and levelness are discussed, and a \texttt{Macaulay2 package, namely \texttt{PolyominoIdeals}, is also presented.
Source: Galois Journal of Algebra
Authors: Ayesha Asloob Qureshi, Francesco Navarra
Institution: Sabancı Üniversitesi
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4416949396
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