2025. \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}. JP Journal of Algebra, Number Theory and Applications. 64, 3 (Mar. 2025), 251–287. DOI:https://doi.org/10.17654/0972555525015.