  We answer the question of how large the dimension of a quantum lens space
must be, compared to the primary parameter $r$, for the isomorphism class to
depend on the secondary parameters. Since classification results in C*-algebra
theory reduces this question to one concerning a certain kind of
$SL$-equivalence of integer matrices of a special form, our approach is
entirely combinatorial and based on the counting of certain paths in the graphs
shown by Hong and Szyma\'nski to describe the quantum lens spaces.
