Title: Searches for multi-Z boson productions and anomalous gauge boson couplings at a muon collider

Abstract: Multi-boson productions can be exploited as novel probes either for standard model precision tests or new physics searches, and have become one of those popular topics in the ongoing LHC experiments, and in future collider studies, including those for electron-positron and muon-muon colliders. Here we focus on two examples, i.e., ZZZ direct productions through $\mu^{+}\mu^{-}$ annihilation at a 1 TeV muon collider, and ZZ productions through vector boson scattering at a 10 TeV muon collider, with an integrated luminosity of $10 \, \text{ab}^{-1}$. Various channels are considered, including, such as $ZZZ \rightarrow 4l2\nu$ and $ZZZ \rightarrow 4l + 2 \text{ jets}$, etc. Expected significance on these multi-Z boson production processes are provided based on a detailed Monte Carlo study and signal background analysis. Sensitives on anomalous gauge boson couplings are also presented.