How many \(7\times 7\) latin squares can be partitioned into Youden squares?
A \(k \times v\) Youden square is a \(k \times v\) array where the set of symbols in the columns of the rectangle are the \(v\) blocks in a symmetric \((v,k, \lambda)\) balanced incomplete block design and in addition the array is row latin. This paper enumerates the number of \(7 \times 7\) latin squares that can be partitioned into a \(3 \times 7\) and a \(4 \times 7\) Youden square. The main results of this paper are that of the 564 isotopy classes of \(7 \times 7\) latin squares, 29 consist of squares that can be partitioned into \(3 \times 7\) and \(4 \times 7\) Youden squares; these 29 isotopy classes belong to 19 of the 147 main classes of \(7 \times 7\) latin squares.
scientific article; zbMATH DE number 744025