2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56495The connection between matrix integrals and links is used to define matrix models which count alternating tangles in which each closed loop is weighted with a factor n, i.e. may be regarded as decorated with n possible colors. For n=2, the corresponding matrix integral is that recently solved in the study of the random lattice six-vertex model. The generating function of alternating 2-color tangles is provided in terms of elliptic functions, expanded to 16-th order (16 crossings) and its asymptotic behavior is given.16 pages. revised: counting up to 16 crossingsMathematical PhysicsHigh Energy Physics - TheoryCombinatoricstext