We determine the maximum number of points in which form exactly distinct triangles, where we restrict ourselves to the case of . We denote this quantity by . It is known from the work of Epstein et al. (Integers 18 (2018), art. id. A16) that . Here we show somewhat surprisingly that and , whenever , and characterize the optimal point configurations. This is an extension of a variant of the distinct distance problem put forward by Erdős and Fishburn (Discrete Math. 160:1-3 (1996), 115–125).
"Characterizing optimal point sets determining one distinct triangle." Involve 13 (1) 91 - 98, 2020. https://doi.org/10.2140/involve.2020.13.91