Connections Between Combinations Without Specified Separations and Strongly Restricted Permutations, Compositions, and Bit Strings

Michael A. Allen

Let $S_n$ and $S_{n,k}$ be, respectively, the number of subsets and $k$-subsets of ${\mathbb{N}}_n=\{1,\dots ,n\}$ such that no two subset elements differ by an element of the set $\…