Counting Multiple Cyclic Choices Without Adjacencies

[摘要] We give a particularly elementary solution to the followingwell-known problem. What is the number of $k$-subsets $X subseteqI_n={1,2,3,dots,n}$ satisfying ``no two elements of $X$ are adjacentin the circular display of $I_n$''? Then we investigate a newgeneralization (multiple cyclic choices without adjacencies) andapply it to enumerating a class of 3-line latin rectangles.

[学科分类] 数学（综合）