A lower bound for the size of the smallest critical set in the back circulant latin square
Cavenagh, N.J. (2006). A lower bound for the size of the smallest critical set in the back circulant latin square. Australasian Journal of Combinatorics, 36, 231- 239.
Permanent Research Commons link: https://hdl.handle.net/10289/3543
The back circulant latin square of order n is the latin square based on the addition table for the integers modulo n. A critical set is a partial latin square that has a unique completion to a latin square, and is minimal with respect to this property. In this note we show that the size of a critical set in the back circulant latin square of order n is at least n ⁴/³/2 - n - n²/³/2 + 2n¹/³ - 1.
Combinatorial Mathematics Society of Australasia (Inc.)
This article has been published in the Australasian Journal of Combinatorics. Used with permission.