Qureshi, Ayesha Asloob; Shibuta, Takafumi; Shikama, Akihiro Simple polyominoes are prime. (English) Zbl 1372.05031 J. Commut. Algebra 9, No. 3, 413-422 (2017). Summary: 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 Gröbner basis with respect to a suitable monomial order. Cited in 1 ReviewCited in 8 Documents MSC: 05B50 Polyominoes 05E40 Combinatorial aspects of commutative algebra 13C05 Structure, classification theorems for modules and ideals in commutative rings 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) Keywords:polyominoes; toric ideals; weakly chordal graphs; Gröbner basis PDF BibTeX XML Cite \textit{A. A. Qureshi} et al., J. Commut. Algebra 9, No. 3, 413--422 (2017; Zbl 1372.05031) Full Text: DOI arXiv Euclid OpenURL