Open Access
2017 Simple polyominoes are prime
Ayesha Asloob Qureshi, Takafumi Shibuta, Akihiro Shikama
J. Commut. Algebra 9(3): 413-422 (2017). DOI: 10.1216/JCA-2017-9-3-413


In this paper, we show that the polyomino ideal of a simple polyomino coincides with the toric ideal of a weakly chordal bipartite graph, and hence, it has a quadratic Gr\"obner basis with respect to a suitable monomial order.


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Ayesha Asloob Qureshi. Takafumi Shibuta. Akihiro Shikama. "Simple polyominoes are prime." J. Commut. Algebra 9 (3) 413 - 422, 2017.


Published: 2017
First available in Project Euclid: 1 August 2017

zbMATH: 1372.05031
MathSciNet: MR3685050
Digital Object Identifier: 10.1216/JCA-2017-9-3-413

Primary: 05E40 , 13C05 , 13P10

Keywords: Gröbner basis , polyominoes , toric ideals , weakly chordal graphs

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

Vol.9 • No. 3 • 2017
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