Totally symmetric Latin squares with prescribed intersection numbers (Q1827738)

A totally symmetric Latin square is a square corresponding to a quasigroup satisfying the identities \(x\cdot y=y\cdot x\) and \(y\cdot (x\cdot y)=x.\) Let \(J[v]\) be the set of numbers \(k\) such that there exist two totally symmetric Latin squares of order \(v\) having exactly \(k\) entries in common. In the paper the set \(J[v]\) is determined for all \(v\geq 2.\)