Przytycki–Vojtěchovský conjecture for cyclic biquandle Yang–Baxter homology

Let $C_m$ be the cyclic biquandle of order $m$, and let $H_n^{NYB}(C_m)$ denote its normalized set-theoretic Yang–Baxter homology group in degree $n$.

Przytycki–Vojtěchovský conjecture.

$$H_n^{NYB}(C_m)=\begin{cases} \mathbb{Z}^{(m-1)^{n-1}}\oplus\mathbb{Z}_m & \text{if $n$ is odd},\\ \mathbb{Z}^{(m-1)^{n-1}} & \text{if $n$ is even}. \end{cases}$$

The paper states that its results partially prove this conjecture by determining the free parts and estimating the torsion parts of the integral set-theoretic Yang–Baxter homology groups of finite cyclic biquandles.