I've been reading the paper on Balanced Sequences and Optimal Routing (Altman, Gaujal, Hordijk; 2000). However, there are a couple of proofs given that I don't quite follow. There are statements made that are assumed to trivially follow, but I can't see how and am hoping someone will be able to help me.(adsbygoogle = window.adsbygoogle || []).push({});

The first is in the proof of Proposition 2.16. The fact that l_i >= (n-1)l_1 + n is easily shown, but 'on the other hand' l_i <= n(l_1) - 3 does not seem to follow from any similar method.

The second is in the proof of Theorem 2.21, Step (2). Where does the fact that |s_1| >= max{4, 2(n+m)+1} come from. (Obviously the 4 is trivial, but I do not understand the 2(n+m)+1)

The paper is attached; I hope that someone with a better understanding than me will be able to follow the proofs and let me know where I'm missing something obvious!

Thanks

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# Balanced Sequences and Optimal Routing

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