Nonsimple polyominoes and prime ideals
Takayuki Hibi, Ayesha Asloob Qureshi
TL;DR
This paper introduces a new class of nonsimple polyominoes for which the associated polyomino ideal remains prime, expanding understanding of the algebraic properties of polyominoes beyond the simple case.
Contribution
It presents a novel class of nonsimple polyominoes with prime polyomino ideals, extending known results from simple polyominoes.
Findings
Identifies a new class of nonsimple polyominoes with prime ideals
Proves the primality of the polyomino ideal for this class
Enhances the algebraic understanding of polyomino structures
Abstract
It is known that the polyomino ideal of a simple polyomino is a prime ideal. A new class of nonsimple polyominoes for which the polyomino ideal is a prime ideal will be presented.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Cholinesterase and Neurodegenerative Diseases