K. Brown [1] studied the random to top shuffle (the Tsetlin libary) by semigroup method. In this paper, (i) we extend his results to the colored permutation groups, and (ii) we consider a q-analogue of Tsetlin library which is different from what is studied in [1]. In (i), the results also extends those results for the top to random shuffle [4],[5], [6] to arbitrary distribution of choosing cards, but we still have derangement numbers in the multiplicity of each eigenvalues. In (ii), a version of q-analogue of derangement numbers by Chen-Rota [3] appears in the multiplicity of eigenvalues.

Mathematics Subject Classification. Primary 35C07; Secondary 35K57.