Class 3 association schemes whose symmetrizations have two classes (Q1347250)

For a given commutative association scheme \(\chi\), by fusing all the non-self-paired relations pairwise with their symmetric counterparts, we can obtain a new symmetric association scheme \(\overline\chi\). The author investigates the case where a symmetric association scheme \(\overline\chi\) of class 2 admits a symmetric commutative fission scheme \(\chi\) of class 3. He shows that there are infinitely many symmetric association schemes of class 2 that admit one or two symmetrizable commutative fission schemes of class 3. These symmetric schemes are then classified and characterized. Some examples are also studied.