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

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.

To appear in Illinois Journal of Mathematics. 20 pages, 16 figures

References in corpus (1)

• Ideals generated by 2-minors, collection of cells and stack polyominoes

Cited by in corpus (4)

• Polyocollection ideals and primary decomposition of polyomino ideals
• On Cohen-Macaulay non-prime collections of cells
• Shellable simplicial complex and switching rook polynomial of frame polyominoes
• Non-simple polyominoes of Kőnig type and their canonical module