Cisto, CarmeloCarmeloCistoNavarra, FrancescoFrancescoNavarraVeer, DharmDharmVeer2025-08-282025-08-282023-02-01https://arxiv.org/abs/2302.08337v1http://repository.iitgn.ac.in/handle/IITG2025/20121In 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.en-USPolyocollection idealsPolyomino idealsBinomial idealsDecompositionClosed path polyominoese-Printe-Print123456789/555