Illinois Journal of Mathematics

Nonsimple polyominoes and prime ideals

Takayuki Hibi and Ayesha Asloob Qureshi

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It is known that the polyomino ideal arising from a simple polyomino comes from a finite bipartite graph and, in particular, it is a prime ideal. A class of nonsimple polyominoes $\mathcal{P}$ for which the polyomino ideal $I_{\mathcal{P}}$ is a prime ideal and for which $I_{\mathcal{P}}$ cannot come from a finite simple graph will be presented.

Article information

Illinois J. Math., Volume 59, Number 2 (2015), 391-398.

Received: 27 July 2015
Revised: 19 November 2015
First available in Project Euclid: 5 May 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13G05: Integral domains 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)


Hibi, Takayuki; Qureshi, Ayesha Asloob. Nonsimple polyominoes and prime ideals. Illinois J. Math. 59 (2015), no. 2, 391--398. doi:10.1215/ijm/1462450707.

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