An Inductive Approach to Constructing Universal Cycles on the k-Subsets of [n]

Abstract

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 $n\ge18$ equivalent to $2 \pmod{8}$, there exists a Universal Cycle on the 4-subsets of [n].