To my understanding the third and fourth sentence "...They are in no specific order. The remaining values are, again in no specific order, on the right of index 2" should be phrased differently: the values before the pivot element are in no specific order but smaller or equal to the pivot element. The remaining valus are again in no specific order but larger than the pivot element.

I have rephrased that sentence to (hopefully) make it clearer. Note that I also changed the example (with *k*=1 the order of the two first elements was always going to be [0,1]).

This is confusing, as you say using k=1 above, but then call it using 2

I updated the text to reflect the (newer) code. Thanks for catching this!