## Illinois Journal of Mathematics

### Nonsimple polyominoes and prime ideals

#### Abstract

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

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

Dates
Revised: 19 November 2015
First available in Project Euclid: 5 May 2016

https://projecteuclid.org/euclid.ijm/1462450707

Digital Object Identifier
doi:10.1215/ijm/1462450707

Mathematical Reviews number (MathSciNet)
MR3499518

Zentralblatt MATH identifier
1341.13010

#### Citation

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