rhj23
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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.
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
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