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In this paper, we introduce a method of constructing Universal Cycles on setsby taking "sums" and "products" of smaller cycles. We demonstrate this newapproach 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 orequal 18 and equivalent to 2 mod 8, there exists a Universal Cycle on the4-subsets of [n].

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