2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115469Any link that is the closure of a positive braid has a natural Legendrian representative. These were introduced in an earlier paper, where their Chekanov--Eliashberg contact homology was also evaluated. In this paper we re-phrase and improve that computation using a matrix representation. In particular, we present a way of finding all augmentations of such Legendrians, construct an augmentation which is also a ruling, and find surprising links to LU-decompositions and Gröbner bases.24 pagesSymplectic GeometryAlgebraic Geometry57R58text