I have (had?) a "collection" of brochures from my shopping around. I was always interested in turfs so that is what I paid attention to and depending on the brochure they were listed as 29x12.00-15 or 31x13.5-15. I thought it might be dependent on age of the brochure where they introduced the line with the smaller tires, then decided to use a larger size.
My operator's manual which is for a TC21D or TC24D (I have the 24), also lists both sizes, one or the other, throughout the manual especially in the specs section. My machine came with the 31x13.5-15.
Another interesting point - there have been discussions here and also stated in the manual that you can adjust the tread setting by dishing in or out. I had mine off to fix a leak and get them loaded and tried dished in, there is only one way the 31x13.5-15 can go on - dished out for the wider setting. Even at that, there is little clearance between the tire and fender for the chains. There is no way they could be mounted dished in, the bolts wouldn't even reach the hub!
So like I said, maybe the machine was originally designed for smaller tires than are currently being shipped.
Brad