Daniel Smith Colors =
Indanthrone Blue (PB 60) + Quinacridone Rose (PV 19)
French Ultramarine (PB 29) + Quinacridone Rose (PV 19)
Mauve by Rembrandt - which is a mix of PV 19 + PB 15 (Quinacridone Violet + Phthalo Blue)
Also Winsor Newton Colors =
Dioxazine Violet (a Cotman color) (PV 23) or Winsor Violet (PV 23)
Cotman is the student grade of Winsor Newton but I've heard people say that some student grade colors are as good as the artist grade.
My Carbazone Violet by Daniel Smith is listed as PV 23 (RS) so not the same as the pure PV 23 that the Winsor Violet but more towards red.
We also got a mix of Ultramarine Deep (Rembrandt? PB 29) and Alizarin Crimson Permanent (not sure of the brand- couldn't find them on the WN site or the DS site so maybe some other manufacturer).
Take some time and find your own favorites - just mix up what you have and play with the colors until you get one you fall in love with and then stick to it - write it down, keep tubes handy, etc. And don't forget, there are certain greens that look so good with violets/purples that it makes your mouth water. Like this photo of a girl in green and purple taken by a flickr member, janchan:
or how about this one by flickr member, patriciawillowcq:
Winsor Newton color (or should I say "colour"?) chart:
Daniel Smith color chart:
Rembrandt color chart: you'll have to check out the sites like Cheap Joe's and Dick Blick for a chart of these colors - they don't seem to have any homepage site themselves.