  We prove that the so-called t algebra of braids and ties supports a Markov
trace. Further, by using this trace in the Jones' recipe, we define invariant
polynomials for classical knots and singular knots. Our invariants have three
parameters. The invariant of classical knots is an extension of the Homflypt
polynomial and the invariant of singular knots is an extension of an invariant
of singular knots previously defined by S. Lambropoulou and the second author.
