On multisets, interpolated multiple zeta values and limit laws

Abstract

In this note we discuss a parameter σ on weighted k-element multisets of [n] = {1, . . . , n}. The sums of weighted k-multisets relate k-subsets, k-multisets, as well as special instances of (truncated) interpolated multiple zeta values, as introduced by Yamamoto [31]. We study properties of this parameter using symbolic combinatorics. We (re)derive and extend certain identities for ζ t ({m} k ), as well as ζ 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.