Universal partial tori
arXiv:2409.12417 · doi:10.1007/s10623-025-01609-9
Abstract
A De Bruijn cycle is a cyclic sequence in which every word of length over an alphabet 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.
19 pages, 1 figure. This version of the article has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10623-025-01609-9