In this paper, we discuss 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 nonsimple polyominoes.
Primality of weakly connected collections of cells and weakly closed path polyominoes
Cisto C.
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2022-01-01
Abstract
In this paper, we discuss 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 nonsimple polyominoes.File in questo prodotto:
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