PreprintCC BY 4.0arXiv
Primality of dilated closed path polyominoes
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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BibTeX
@misc{larney2026primality,
title = {{Primality of dilated closed path polyominoes}},
author = {Niall Larney},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30086},
eprint = {2609.30086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30086},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Primality of dilated closed path polyominoes
AU - Niall Larney
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30086
UR - https://arxiv.org/abs/2609.30086
AB - 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.
ER -