Interesting topic! We are a relatively new daylily farm and have bought about 160 cultivars over the last three years. We try to get double or better but for some, price and availability dictate that single is the only way one can go. We find that singles naturally take longer to multiply than doubles - with doubles, you are starting with twice as many, so increase is a lot faster. However, what I think is the driving force behind increase is two fold. First is fan maturity. A fan that has been around for a couple of years is a lot faster to multiply than a new fan. The second factor touches on the "divide/not divide" question. If you divide a double fan, you are stressing the two fans a lot - they are literally chopped in half, lose a lot of their roots and have to recover underground before doing great things above ground and multiplying.
So in summary, I think that the best scenario is to get two (or even one) mature single fans that are "whole" rather than two single fans that were recently separated. A mature single or double fan will also establish and multiply nicely. I think that the worst thing to get when receiving new cultivars is tiny single fans with a couple of small roots. It can be a challenge to keep these alive, much less worry about blooms and increase.
One more note. The thing that I dislike most about getting new cultivars is when the vendor ships multiple small fans rather than a mature double (or single) and because the fans are small and young, it is likely that you don't see a bloom that year (up here anyhow). Then the ultimate disappointment is when the plant does bloom the following year it is the wrong cultivar!!
Sorry for the rant - I vote for mature single or double fans.
Cheers,
