2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131491We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. generating function for counting bicolored discrete surfaces with non uniform boundary conditions. As an application, we prove the $x-y$ symmetry of the algebraic curve invariants introduced in math-ph/0702045.37 pages, latexMathematical PhysicsHigh Energy Physics - TheoryTopological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariantstext