论文信息 - Multicover Ucycles

Multicover Ucycles

A Universal Cycle, or Ucycle, for k-subsets of n]=1, 2, ?, n is a cyclic sequence of (kn) integers with the property that every k subset of n] appears exactly once consecutively in the sequence. A t-cover Ucycle for k-subsets of n] is a cyclic sequence of t(kn) integers with the property that every k-subset of n] appears exactly t times consecutively in the sequence. Here we investigate the minimal number t=U(n, k) for which there is a t-cover Ucycle.

Glenn H. Hurlbert | G. Hurlbert

[1] de Ng Dick Bruijn. A combinatorial problem , 1946 .

[2] Bradley W. Jackson. Universal cycles of k-subsets and k-permutations , 1993, Discret. Math..

[3] David Singmaster,et al. Notes on Binomial Coefficients I—A Generalization of Lucas' Congruence , 1974 .

[4] H. Fredricksen. A Survey of Full Length Nonlinear Shift Register Cycle Algorithms , 1982 .

[5] Fan Chung Graham,et al. Universal cycles for combinatorial structures , 1992, Discret. Math..