An Erdős-Ko-Rado Theorem for Permutations with Fixed Number of Cycles

@article{Ku2014AnET,
  title={An Erdős-Ko-Rado Theorem for Permutations with Fixed Number of Cycles},
  author={Cheng Yeaw Ku and Kok Bin Wong},
  journal={Electr. J. Comb.},
  year={2014},
  volume={21},
  pages={P3.16}
}
Let Sn denote the set of permutations of [n] = {1, 2, . . . , n}. For a positive integer k, define Sn,k to be the set of all permutations of [n] with exactly k disjoint cycles, i.e., Sn,k = {π ∈ Sn : π = c1c2 · · · ck}, where c1, c2, . . . , ck are disjoint cycles. The size of Sn,k is [ n k ] = (−1)n−ks(n, k), where s(n, k) is the Stirling number of the… CONTINUE READING