Recently, Kenyon and Wilson introduced a certain matrix M in order to compute pairing probabilities of a double-dimer model. They showed that the absolute value of each entry of the inverse matrix of M is equal to the number of certain Dyck tilings of a skew shape. They conjectured two elegant formulas on the sum of the absolute values of the entries in a row or a column of M^{-1}. In this talk we will see bijective proofs of the two conjectures due to Kim, Meszaros, Panova, and Wilson. In the two bijective proofs Dyck tilings correspond to increasing labelled trees and complete matchings. We will also see a connection between Dyck tilings and the (q,t)- Catalan numbers.