Illinois Journal of Mathematics

Nonsimple polyominoes and prime ideals

Takayuki Hibi and Ayesha Asloob Qureshi

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1462450707

Digital Object Identifier
doi:10.1215/ijm/1462450707

Mathematical Reviews number (MathSciNet)
MR3499518

Zentralblatt MATH identifier
1341.13010

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

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


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