1850, Kirkman, a regional director of the Church of England, raised an interesting question: a female teacher took her 15 female students for a walk every afternoon. She divided the students into five groups with three people in each group and asked how to arrange it so that every two students could be in the same group only one day a week. Kirkman himself gave the answer to this question in the second year. But this is only the case of n = 15. When n is an arbitrary divisible positive integer, the necessary and sufficient conditions for the above grouping to be realized have not been proved. This is a necessary and sufficient condition for the existence of combinatorial design, and 100 has not been solved for many years.

In memory of Kirkman who studied mathematics by herself, people called this famous mathematical problem "Kirkman girl problem".

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1961-1978, Lu Jiaxi successively wrote several papers about this achievement, such as The Method of Making Kirkman Series and Steiner Series, The Method of Constructing Balanced Incomplete Blocks and Decomposable Incomplete Blocks, etc., but it has not been published for various reasons. During the period of1April, 979, he came across the authoritative journals of combinatorial mathematics published in 1974 and 1975 in the United States, and found that the Kirkman problem and its generalization of four-tuple series had been published in 197 1 and 1972.