Cisto, CarmeloCarmeloCistoNavarra, FrancescoFrancescoNavarraVeer, DharmDharmVeer2025-08-312025-08-312024-03-0110.1016/j.jalgebra.2023.11.0242-s2.0-85179034029https://d8.irins.org/handle/IITG2025/26436In 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.truePolyominoes | Primary decomposition | Zig-zag walkArticlehttps://doi.org/10.1016/j.jalgebra.2023.11.0241090266X498-5291 March 20244arJournal3