English

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

Commutative Algebra 2022-08-30 v3 Combinatorics

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.

Keywords

Cite

@article{arxiv.2106.02155,
  title  = {Primality of weakly connected collections of cells and weakly closed path polyominoes},
  author = {Carmelo Cisto and Francesco Navarra and Rosanna Utano},
  journal= {arXiv preprint arXiv:2106.02155},
  year   = {2022}
}

Comments

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