Universal partial tori
<|reference_start|>Universal partial tori: A De Bruijn cycle is a cyclic sequence in which every word of length $n$ over an alphabet $\mathcal{A}$ appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. We find them computationally and construct infinitely many of them using one-dimensional variants of universal cycles, including a new variant called a universal partial family.<|reference_end|>
@article{carey2024universal,
    title={Universal partial tori},
    author={William D. Carey, Matthew Kearney, Rachel Kirsch, and Stefan Popescu},
    journal={arXiv preprint arXiv:2409.12417},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12417},
    primaryClass={math.CO cs.DM}
}