For those who are members of the AHS - American Hemerocallis Society.
The AHS has an archive of nearly all of the Daylily Journals on its member web-site.
In one of the issues there is an article describing how one can increase daylily fans without the use of plant hormones by cutting the crown into pieces. It does suggest that using a fungicide will help prevent the loss of some of the newly developing fans.
The title is "Propagation of Hemerocallis by ramet cuttage". It is in Volume 21, Number 2, 1967 beginning on page 44.