An inductive approach to constructing Universal Cycles on the k-subsets of [n]

In this paper, we introduce a method of constructing Universal Cycles on sets by taking "sums" and "products" of smaller cycles. We demonstrate this new approach by proving that if there exist Universal Cycles on the 4-subsets of [18] and the 4-subsets of [26], then for any integer n which is greater than or equal 18 and equivalent to 2 mod 8, there exists a Universal Cycle on the 4-subsets of [n].