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_{i}}

_{i=1,n}being the probability distribution, I want to show that a Huffman reduction cannot be decreasing, and I reached a point where I need to show that

q+H(p

_{1},...,p

_{n-s},q) ≥ H(p

_{1},...,p

_{n}), where

q = p

_{n-s+1}+ ... + p

_{n}and s is chosen such that: 2 ≤ s ≤ m (m≥n) and s = n (mod(m-1))

where m is the number of m-arr symbols from a Huffmann m-arr algorithm.