Year: 2020
Type: article
Abstract: It is known that the polyomino ideal of simple polyominoes is prime. In this paper, we focus on multiply connected polyominoes, namely polyominoes with holes, and observe that the nonexistence of a certain sequence of inner intervals of the polyomino, called zig-zag walk, gives a necessary condition for the primality of the polyomino ideal. Moreover, by computational approach, we prove that for all polyominoes with rank less than or equal to 14 , the above condition is also sufficient. Lastly, we present an infinite new class of prime polyomino ideals.
Source: Illinois Journal of Mathematics
Authors: Carla Mascia, Giancarlo Rinaldo, Francesco Romeo
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2962897917