Lemmas aside, how is this different than only checking repeated prime cycles in conjunction with one of the existing partition algorithms like NAUTY? Laci perso

Lemmas aside, how is this different than only checking repeated prime cycles in conjunction with one of the existing partition algorithms like NAUTY? Laci personally rejected my note submitted to Information Processing Letters saying the lower bound formula was "trivial", https://oeis.org/A186202 https://oeis.org/A186202