I have previously hatched chicks that are grown and a couple of the boys have a carnation comb, a walnut comb, and a rose comb. I do have a hen and rooster with a rose comb, but neither of them were the parent of the chicks I hatched previously, lol. It is amazing to me that it is possible for some of my straight combed boys to have a walnut combed parent in their gene pool or a rose comb. Two of my boys ended up with carnation combs and I only have one hen with a carnation comb and she lays olive eggs. No olive eggs in that hatch though!! Crazy!
If you want a basic rundown of the rose and pea comb genetics, I see they are in this article:
https://poultry.extension.org/articles/poultry-anatomy/poultry-genetics-an-introduction/
I think that one neglects to mention that two pea comb genes will usually make the comb smaller than one pea comb gene, and will also shrink the wattles.
I don't see duplex comb in that article either (Buttercup or V comb). It is controlled by a different gene than rose or pea, but it's hard to find information about how it interacts with them.
Carnation comb is (as best I can tell) genetically a single comb with side sprigs (little bits that stick out at the back edge.) I haven't been able to find anything on the genes that cause side sprigs, except that they are genetically controlled rather than simply random.
There is a linkage between the pea comb gene and the blue egg gene. They are near each other on the chromosome, so they tend to be inherited together. They can be linked in any combination:
pea comb, blue egg (example: Ameraucana)
pea comb, not-blue egg (example: Brahma)
not-pea comb, blue egg (example: Cream Legbar)
not-pea comb, not-blue egg (example: Marans, Leghorn, Wyandotte, Polish, all other breeds that lay brown or white eggs and have a single, rose, or duplex comb)
Because of the linkage, pea comb or lack of it can sometimes be used to track the blue egg gene in breeding programs.