Carpathian Journal of Mathematics, Vol. 34, No. 2 (2018), pp. 143-155 (13 pages) In the paper, we extend known results concerning crossing numbers for join of graphs of order six. We give the crossing ...

Let the random variable $Z_{n,k}$ denote the number of increasing subsequences of length k in a random permutation from $S_{n}$, the symmetric group of permutations ...