How works the saturation at the level of the pixels?

Hello,
I have a good idea of how the digital system works: a photosite that becomes a pixel by the matrix system bayer.
I see clearly the effect of brightness and of course of the contrast but I do not understand how the saturation adjustment works.
Can anybody help me?

tks

Saturation is just like contrast. However, unlike the usual contrast that increases the separation between dark and light parts of an image, saturation increases the separation between different shades of colours in the image.

Saturation is essentially a measure of the difference between the red, green, and blue channel values. A perfectly grey pixel has identical values in all of the channels, A highly saturated pixel has a big difference between the maximum channel value and the minimum channel value.

So to reduce saturation you bring the channel values closer to the average value of the channels, and to increase saturation you move the values further away from the average.

Thanks a lot for your answers…
It is obviously my problem : in my mind : increasing the value of all pixels of a color (s), seems to me to increase the luminosity and not the density of the color (s)… ?
Where is my error ?

It depends on das color model.

I didn’t find a nice diagram for the subtractive color space CMYK.

Consider a pink pixel. If we want to increase the saturation so it will appear more red, then we must increase the red value, and to keep the same brightness we reduce the green and blue values.

:o)

Thanks a lot,
Using GIMP, I made a new picture full of pink color.
I adjusted the saturation and I have been observing on the histogram what you said, and it is very clear !
Again, tks

ps :I’m not sur that my grammar is correct :o(((