Yeah, Mauve is the combination of both blue and chocolate genes expressing. Chocolate is sexlinked, so how it's inherited depends on whether the male or the female is the Chocolate individual in the pairing. To make Mauves right away, you want a Chocolate male:
Chocolate male x Blue female = 25% Black males carrying chocolate, 25% Blue males carrying chocolate, 25% Chocolate females, and 25% Mauve females
Chocolate male x Splash female = 50% Blue males carrying chocolate, 50% Mauve females
The other way around, you don't get any Mauves in the first generation cross, but could use the male offspring from such a cross to make Mauves in the future:
Blue male x Chocolate female = 25% Black males carrying chocolate, 25% Blue males carrying chocolate, 25% Black females, 25% Blue females.
Splash male x Chocolate female = 50% Blue males carrying chocolate, 50% Blue females
Remember that females
cannot carry the chocolate gene, so in this second set of birds only the males carry the chocolate gene and the females do not have it at all!
To get Mauve males, you'll have to do an additional cross, either using any of the males carrying chocolate crossed to the Mauve females, or using the Blue males carrying chocolate crossed to Chocolate females.
Black male carrying chocolate x Mauve female = 25% Blue offspring, 25% Black offspring, 25% Chocolate offspring, and 25% Mauve offpsring, in each case of both sexes.
Blue male carrying chocolate x Mauve female = 25% Blue offspring, 25% Mauve offspring, 12.5% Splash offspring, 12.5% Mauve Splash offspring, 12.5% Black offspring, and 12.5% Chocolate offspring, in each case of both sexes.
Blue male carrying chocolate x Chocolate female = the exact same results as the Black male carrying chocolate x Mauve female.
Now, having your Blues and Splashes that potentially carry recessive white in there means that whites could pop up in this generation of crossings in addition to the colors listed. Effectively, you'd have the same ratios of each color that I listed, but about one quarter of each color would express White instead
if both parents in the cross happen to carry recessive white.
And, about equal numbers of each color should be frizzled and non-frizzled from each cross where your frizzle is involved, assuming that you always cross frizzle to smooth as is always recommended.
I agree with this as well.