Polyocollection ideals and primary decomposition of polyomino ideals
Commutative Algebra
2023-12-06 v2 Combinatorics
Abstract
In this article, we study the primary decomposition of some binomial ideals. In particular, we introduce the concept of polyocollection, a combinatorial object that generalizes the definitions of collection of cells and polyomino, that can be used to compute a primary decomposition of non-prime polyomino ideals. Furthermore, we give a description of the minimal primary decomposition of non-prime closed path polyominoes. In particular, for such a class of polyominoes, we characterize the set of all zig-zag walks and show that the minimal prime ideals have a very nice combinatorial description.
Cite
@article{arxiv.2302.08337,
title = {Polyocollection ideals and primary decomposition of polyomino ideals},
author = {Carmelo Cisto and Francesco Navarra and Dharm Veer},
journal= {arXiv preprint arXiv:2302.08337},
year = {2023}
}
Comments
To appear in Journal of Algebra. 24 pages, 16 figures