Planar networks and total positivity of Riordan arrays

In 2015, Chen, Liang and Wang provided several sufficient conditions for the total positivity of Riordan arrays and asked for combinatorial proofs of these results. In this paper, we present such proofs by constructing suitable planar networks with non-negative weights and applying the Lindström-Gessel-Viennot lemma. Moreover, we slightly generalize one of the results and give more totally positive Riordan arrays.