“\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, vol. 64, no. 3, Mar. 2025, pp. 251-87, https://doi.org/10.17654/0972555525015.