UNIVERSAL CYCLES OF K-SUBSETS AND K-PERMUTATIONS

In this paper the author constructs universal cycles of 3-subsets of a n n-set for n greater-than-or-equal-to 8 and (n, 3) = 1, verifying a c onjecture of Chung et al. (1989) for 3-subsets. Universal cycles of 4- subsets of an n-set for n greater-than-or-equal-to 8 and (n, 4) = 1 ar e also constructed, partially solving the same conjecture for 4-subset s. Universal cycles of k-permutations are constructed for any k greate r-than-or-equal-to 3 and n greater-than-or-equal-to k + 1.