Polyocollection ideals and primary decomposition of polyomino ideals

Autor:	Cisto, Carmelo, Navarra, Francesco, Veer, Dharm
Rok vydání:	2023
Předmět:	Mathematics - Commutative Algebra Mathematics - Combinatorics 05B50 05E40
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jalgebra.2023.11.024
Popis:	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. Comment: To appear in Journal of Algebra. 24 pages, 16 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.08337 Zobrazit plný text záznamu View this record from Arxiv