# On multisets, interpolated multiple zeta values and limit laws

## TL;DR

This paper explores a parameter on weighted multisets, connecting it to multiple zeta values and deriving new identities, while also analyzing the distribution and limit laws of associated random variables.

## Contribution

It introduces a new parameter on multisets, extends identities for interpolated multiple zeta values, and studies their probabilistic limit laws using symbolic combinatorics.

## Key findings

- Derived new identities for interpolated multiple zeta values.
- Established distributional properties of random variables on multisets.
- Proved limit laws as parameters grow large.

## 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 $\zeta^{t}_n(\{m\}_k)$. 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.