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arXiv · 1907.08438

Primality of multiply connected polyominoes

Carla Mascia·Giancarlo Rinaldo·Francesco Romeo
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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 non-existence 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 class of prime polyomino ideals.

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Carla Mascia, Giancarlo Rinaldo, Francesco Romeo. 2019-07-19. Primality of multiply connected polyominoes. https://doi.org/10.1215/00192082-8591560

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