Perfect 1-factorisations of K16
We report the results of a computer enumeration that found that there
are 3155 perfect 1-factorisations (P1Fs) of the complete graph K16.
Of these, 89 have a non-trivial automorphism group (correcting an earlier
claim of 88 by Meszka and Rosa).
We also (i) describe a new invariant which distinguishes between the
P1Fs of K16, (ii) observe that the new P1Fs produce no atomic
Latin squares of order 15 and (iii) record P1Fs for a number of large
orders that exceed prime powers by one.