Permanent link to Research Commons versionhttps://hdl.handle.net/10289/15662
The full n-Latin square is the n × n array with symbols 1, 2,..., n in each cell. In a way that is analogous to critical sets of full designs, a critical set of the full n-Latin square can be used to find a defining set for any Latin square of order n. In this paper we study the size of the smallest critical set for a full n-Latin square, showing this to be somewhere between (n3 − 2n2 + 2n)/2 and (n − 1)3 + 1. In the case that each cell is either full or empty, we show the size of a critical set in the full n-Latin square is always equal to n3 − 2n2 − n.
SPRINGER JAPAN KK