数独矩形补全
Sudoku Rectangle Completion
摘要：
在过去的十年里，数独，一个组合数字位置的难题，已经成为世界各地许多人最喜欢的消遣。在这个谜题中，任务是完成一个部分填充的$9 \times 9$正方形，其中包含数字1到9，但每个数字必须在每行、每列和九个$3 \times 3$方块中出现一次。数独方可以被认为是拉丁方的一个子类。本文研究了关于拉丁方补的一个经典结果到数独方的自然扩张。此外，我们使用的证明中开发的程序，以获得的顺序$n$数独广场的数量的渐近界。
英文摘要：
Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9 \times 9$ square with numbers 1 through 9, subject to the constraint that each number must appear once in each row, each column, and each of the nine $3 \times 3$ blocks. Sudoku squares can be considered a subclass of the well-studied class of Latin squares. In this paper, we study natural extensions of a classical result on Latin square completion to Sudoku squares. Furthermore, we use the procedure developed in the proof to obtain asymptotic bounds on the number of Sudoku squares of order $n$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
