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arXiv · 2106.02155

Primality of weakly connected collections of cells and weakly closed path polyominoes

Carmelo Cisto·Francesco Navarra·Rosanna Utano
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Abstract

In this paper we study the primality of weakly connected collections of cells, showing that the ideal generated by inner 2-minors attached to a weakly connected and simple collection of cells is the toric ideal of the edge ring of a weakly chordal bipartite graph. As an application of this result we characterize the primality of the polyomino ideals of weakly closed paths, a new class of non simple polyominoes.

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Carmelo Cisto, Francesco Navarra, Rosanna Utano. 2021-06-03. Primality of weakly connected collections of cells and weakly closed path polyominoes. https://doi.org/10.1215/00192082-10123611

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