Statistics of Blocks in k-Divisible Non-Crossing Partitions
Statistics of Blocks in k-Divisible Non-Crossing Partitions
We derive a formula for the expected number of blocks of a given size from a non-crossing partition chosen uniformly at random. Moreover, we refine this result subject to the restriction of having a number of blocks given.Furthermore, we generalize to $k$-divisible partitions. In particular, we find that, asymptotically, the …