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I am trying to understand Gjergji Zaimi's answer in What are the periodic Dyck paths?. In the third paragraph he claims that Next, we define the matrix $X_D$ similarly to the Cartan matrix except we ...

(This question can be formulated purely combinatorially in terms of Dyck paths, which is done in the second part of the question. But I am more interested whether this can be explained by some sort of ...

I changed the thread completely so that everything is now elementary linear algebra. A Dyck path of length $n$ is a list of positive integers $[c_1,c_2,...,c_n]$ with $c_i -1 \leq c_{i+1}$ for all $i$...