Subsquares in generalized sudoku squares.

摘要

The question, for what orders does there exist a subsquare-free latin square, has not been completely solved to date. We wish to extend the problem of finding subsquare-free latin squares to generalized sudoku squares. We give an attempted solution by constructing a generalized sudoku square with no subsquares of order m, where m ∉{2, n}. Additionally, when n ≠ 2 or 4, we give a construction for a generalized sudoku square of order n 2 with no intercalates.