On multisets, interpolated multiple zeta values and limit laws

Abstract

In this work we discuss a parameter $\sigma$ on weighted $k$-element multisets of $[n]=\{1,\dots ,n\}$. 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 rederive and extend certain identities for ${\zeta }_n^t(\{m{\}}_k)$. 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.

24 pages, no figure; final version to appear in Electronic Journal of Combinatorics