Exercise problem 2.4
I'm stuck at the exercise problem 2.4 behind the book despite the hint. My approach is to characterize the B(N+1,K) >= recursion as an upper bound on the lower order (in N) terms and then follow the approach of proving the Sauer lemma. However I'm stuck on constructing the "specific set" of dichotomies. I fail to see how the special property to this set (limiting the number of 1 as hinted) can make this proof go easier.
I'm not very good at mathematical proofs so any additional hints will be greatly appreciated.
