On multisets, interpolated multiple zeta values and limit laws

In this work we discuss a parameter a on weighted k-element multisets of [n] = {1, ..., n}. The sums of weighted k-multisets are related to k-subsets, k-multisets, as well as special instances of truncated interpolated multiple zeta values. We study properties of this parameter using symbolic combinatorics. We (re)derive and extend certain identities for zeta(t)(n)({m}(k)). Moreover, we introduce random variables on the k-element multisets and derive their distributions, as well as limit laws for k or n tending to infinity.