SL2-tilings and triangulations of the strip

SL 2 -tilings were introduced by Assem, Reutenauer, and Smith in connection with frieses and their applications to cluster algebras. An SL 2 -tiling is a bi-infinite matrix of positive integers such that each adjacent 2 × 2 -submatrix has determinant 1. s paper we define the class of SL 2 -tilings with enough ones. It contains the previously known tilings as well as some which are new, and we show that it is in bijection with a certain class of combinatorial objects, namely “good” triangulations of the strip.