\begin{aligned} & \text { A } \mathbb{Z} \text {-BASIS OF THE } S_n \text {-INVARIANT SUBRING } \\ & \text { OF } \mathbb{Z}\left[a_i-a_j\right] \end{aligned}. JPJANA 2025, 64 (3), 251-287. https://doi.org/10.17654/0972555525015.