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arXiv · 2609.30086

Primality of dilated closed path polyominoes

Niall Larney
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Abstract

In this paper we define a novel product on polyominoes called the tensor product of polyominoes. Using a special case of this product which we name a dilation, we construct a new class of polyominoes called the dilated closed paths. This class is a ''thick'' generalization of Cisto and Navarra's class of closed paths (arXiv:2006.13935). We prove the Zig-Zag Walk Conjecture for this new class thereby fully characterizing primality for its associated polyomino ideals.

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Niall Larney. 2026-09-24. Primality of dilated closed path polyominoes. https://arxiv.org/abs/2609.30086

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