On the properties of alternating invariant functions

Haiqing Zhu, Su Hu, Min-Soo Kim

Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$}, \end{align*} are named the…