Cavenagh, N. J., & Raass, V. (2016). Critical sets of 2-balanced Latin rectangles. Annals of Combinatorics, 1–14. https://doi.org/10.1007/s00026-016-0322-0
Permanent Research Commons link: http://hdl.handle.net/10289/11297
An (m, n, 2)-balanced Latin rectangle is an (Formula presented.) array on symbols 0 and 1 such that each symbol occurs n times in each row and m times in each column, with each cell containing either two 0’s, two 1’s or both 0 and 1. We completely determine the structure of all critical sets of the full (m, n, 2)-balanced Latin rectangle (which contains 0 and 1 in each cell). If m, (Formula presented.), the minimum size for such a structure is shown to be (Formula presented.). Such critical sets in turn determine defining sets for (0, 1)-matrices.
This is an author’s accepted version of an article published in the journal: Annals of Combinatorics. © 2016 Springer International Publishing.