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I am trying to learn the amalgamation of two cluster seeds and I am reading the paper https://arxiv.org/pdf/math/0508408.pdf written by V.V. Fock and A. B. Goncharov. I am at a loss for the Lemma 2.2. on page 9.enter image description here

My question is (a) I don't find a function $c$ on $K$.

(b) I don't understand the proof of Lemma 2.2, who can explain it clearly? Or offer me some relative papers. Any help will be appreciated.

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  • $\begingroup$ I don't know why someone vote down my question? Maybe this question is very clear but I just want to get some relative papers and helps to solve this question. $\endgroup$
    – Daisy
    Commented Jun 5, 2017 at 3:12
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    $\begingroup$ This seems to be a misprint. The $c$ should be a $d$ and also $s\in C$ should be $s\in K$. Then the existence of $d$ is just what is stated in condition (iii) and uniqueness is obvious because the $I(s)$ cover $K$. $\endgroup$
    – ThiKu
    Commented Jun 5, 2017 at 3:56

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